
Book___^ 



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COPXRIGHT DEPOSIT 



THE PRACTICAL 

SURVEYOR'S GUIDE. 



CONTAINING 



THE NECESSARY INFORMATION TO MAKE ANT PERSON OF 

COMMON CAPACITY A FINISHED LAND SURVEYOR, 

WITHOUT THE AID OF A TEACHER. 



BY 

ANDREW DUNCAN", 

Land Surveyor and Civil Engineer, 



A NEW, REVISED AND GREATLY ENLARGED EDITION. 



ILLUSTRATED BY SEVENTY-TWO ENGRAVINGS. 



/^6 



PHILADELPHIA : 

HBNEY CABBY BAIRD & CO., 

Industrial Publishers, Booksellers and Importers, 

810 Walnut Street. 

1892. 



Copyright, by 

HENRY CAREY BAIRD & CO., 

1892. 



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6^ 



,-^n 



PRINTED AT 

COLLINS PRINTING HOUSk, 

PlllLADBLFMIA, U. S. A. 



^-::?$?-7<r y 



PREFACE TO THE REVISED EDITION. 



As shown by the constant demand for it, '" The 
Practical Survbyoe's Guide" still maintains the 
popularity and reputation it has, for so many years, 
enjoyed. 

The issue of a new edition having become neces- 
sary, a considerable amount of new matter has 
been added in order to make the work still more 
useful to the reader. No changes, except neces- 
sary corrections, have been made in the original 
text. 

The greater portion of the new matter has been 
translated from " Katechismus der Feldmesskunst," 
by Dr. C. Pietsch, a very popular German work 
which has passed through five editions. In making 
these additions, the aim of the author of the original 
work — to prepare a book sufficiently concise and 
instructive in the several details — has been con- 
stantly kept in view. 

(iii) 



IV PREFACE TO THE REVISED EDITION. 

It is hoped that this new edition may prove of 
value to surveyors, professional and unprofessional, 
in giving them the needed information in a clear 
and simple manner, unburdened with unnecessary 
matter. 

Philadelphia, November 15, 1892. 



PREFACE TO THE FIRST EDITION. 



The following compilation is made in conseq-nnce of tlia 
undersigned not having met with any work or. >i j ir'^i- 
sofficiently concise, and instructive in the several details, 
necessary to qualify properly the practical surveyor. Many 
of the works already published contain subjects not neces- 
sary in such treatises ; such as Geometry, Plane Trigo- 
nometry, &c., which subjects, it is taken for granted, all 
who intend to become proficients have studied prior to 
reading Surveying. They are also found not to contain 
instruction that in recent improvements the surveyor re- 
quires to know. Many of these things the compiler of this 
short treatise, will endeavour to supply ; also, many other 
necessary things, which, in his long experience, he has 
found indispensable to the correct practitioner. He has 
collected the most necessary instruction in leveling and 
profiling, with a new and speedy plan of setting grades 
on rail and plank roads. The method of inflecting curves, 
not hitherto sufficiently explained. The description and 
design of a new instrument whereby distances are found 
at once without any calculation. A new method of sur- 
veying any tract of land by measuring one line through 
it, with a geometrical demonstration of the same. A geo- 
metrical method of correcting surveys taken with the Com- 

(V) 



VI PREFACE TO THE FIRST EDITION. 

pass, to fit them for calculation, with a table of corrections 
for certain distances, but applicable to all. A short naethod 
of finding the angles from the courses, and vice versa. 
The method of surveying with the Compass through any 
mine or iron works, and to correct the deflections of the 
needle by attraction. Description of an instrument by the 
help of which any gentleman may measure a map by inspec- 
tion, without calculation. A new and short method of calcu- 
lation, wherein fewer figures are used than in the common 
method ; also, the Pennsylvania method. Tables of diflfer- 
ence of Latitude and Departure, made expressly for two 
pole chains, but which can also be used with four poles. 
The method of correcting the diurnal variation of the 
needle, most useful in tracing the boundaries of surveys, 
a complete description of which is given with the reason 
for using 57-3° and how it is found. Various methods of 
plotting and embellishing maps. The most correct method 
of laying off lots with a pole, plummets, &c. Description 
of a new Compass which the compiler has contrived for 
that purpose, and which is made by Eeid & Sons, Smith- 
field street, Pittsburgh. 

The compiler does not deny that he lias borrowed from 
many authors those things he has found best adapted to 
the completion of a work adequate to make a finished 
American Surveyor, of which an unprejudiced and en- 
lightened public are the best judges. 

ANDREW DUNCAN, 

Land Surveyor and Civil Engineer, 

Office, Odeon Building, Fourth St., Pittshurgh. 



CONTENTS 



INTRODUCTION. 

PAGB 

Object of surveying; What a survey should include. 17 
Definition of points ; Determination of a straight line 

and of a plane surface ; Map of a survey 18 

Scales according to which maps of surveys are drawn . . 19 

INSTRUMENTS FOE MEASURING DISTANCES AND 
THEIR USE. 

Mode of indicating a point in the field; Manner of mark- 
ing a point in the field; Boundary stones 20 

Pins and poles for marking; Establishment of a straight 
line in the field; To find a point lying in the prolonga- 
tion of a straight line • • . . . 21 

Two points, A and B, marked by poles, being given, to 
find a point of the straight line AB, which lies be- 
tween A and B 23 

Signals and their meaning 24 

Manner of setting poles ; To find the point C of the 
straight line AB, which lies between A and B, with- 
out the help of an assistant ; How to determine a point 
in the straight line AB, when it is impossible to take 

position in the prolongation of AB 25 

Length of a straight line 27 

Measuring rods and their use 28 

How to measure with the measuring rods a line which is 

not horizontal 29 

(vii) 



vill CONTENTS. 

PAGE 

The tape measure and its appurtenances 30 

Mode of measuring with the tape 31 

Marking pins 32 

Determination of the distance A B when measuring is 

prevented by an obstacle between A and B 33 

To find the length A B when the straight line A B passes 

through a pond or forest 34 

How to find the distance A B when the straight line A B 

continues across a river 36 

Two points A and B are given; between A and B lies a 
forest. The direction of the straight connecting line 
" of these points is to be determined in A and B . . . . 38 

Chains; Gunter's link 39 

Ordinary surveyor's chain ; Grumman's patent chains . . 40 

Vara chains; Metre chains; Marking pins 41 

Content of an acre; Manner of reducing the contents of a 
piece of land, when given in square links, to acres, 

roods and perches 42 

Various methods of measuring distances; Wheel pedome- 
ters; Pacing and pedometer 43 

Different kinds of pedometers ; Mode of pacing 44 

Guessing or judging distance , 45 

INSTRUMENTS FOR SETTING-OUT RIGHT ANGLES, 
AND THEIR USE. 

Surveyor's cross, or cross staff 46 

The cross staff head 47 

Problems which may be solved with the assistance of 

either of the above-mentioned instruments 48 

How to erect a perpendicular at the point C in the 
straight line A B ; How to let fall a perpendicular to a 
straight line A B from a point C 49 



CONTENTS. IX 

PAGE 

How to determine an intermediate point C in the straight 
line A B 50 

To test whether the visual planes of the two sights stand 

perpendicularly one upon the other 51 

Surveyor's angle-mirror , "" 

Laws of the reflection of light by plane mirrnrs ^4 

Axis of incidence; Angle of incidence; ^\Tjgle of reflec- 
tion; Explanation of the mode of oj ■'.■ ■ ■ ' • 

angle-mirror , . . . . 55 

Use of the angle-mirror 58 

How to erect with the assistance of the angle-mirror a 
perpendicular to the straight line A B at a point C in 

the latter 59 

How to let fall with the assistance of the angle-mirror a 
perpendicular C D from a point C to a straight line 

AB 60 

How to find with the assistance of the angle-mirror an 

intermediate point in the straight line A B 62 

Testing the angle- mirror as to its accuracy 64 

Prism for right angles 65 

Use of the prism 66 

To set out right angles with the tape measure alone. . . 67 
Given, two points A and B, which are separated by an 
obstacle which cannot be seen through, for instance, a 
foiest. To determine their connecting line in the 

points A and B, as well as the length of A B 69 

Given, a straight line A B passing across a lake; its 

length is to be determined 71 

A given straight line A B strikes in its prolongation an 
obstacle, which cannot be seen through, for instance, a 
house ; to find the prolongation on the other side of this 

obstacle 72 

A straight line A B is given. From a point C a perpen- 



X CONTENTS. 

PAGE. 

dicular is to be let fall to the straight line, the direct 
execution of the operation being, however, rendered 
impossible by an intervening building *13 

SURVEY OP SMALLER TRACTS WITH THE ASSISTANCE 
OF THE PREVIOUSLY-DESCRIBED INSTRUMENTS. 

To survey a three-sided field 16 

To survey a many-sided field or polygon 77 

Noting the results of the measurements 79 

PROBLEMS. 

To reduce two pole chains and links to four pole ones ; 
To reduce four pole chains and links to two pole ones . 81 

Areas; To find the content oi" a square 82 

To find the area of a parallelogram 83 

The content of an oblong piece of ground and one side 

being given, to find the other 84 

To find the content of a trapezium 86 

Various rules for finding the content of a triangle. ... 87 

To find the area of a trapezoid, rule 99 

To find the area of a trapezium when each side and the 

angle of intersection of the diagonals are given. . . . 101 
To find the area of a trapexium, when the four sides are 
severally given, and also the sum of any two opposite 

angles 102 

To find the area of a circle having the diameter given ; 
To find the area of an ellipsis ; To find the area of a 
parabola ; To find the area of a segment of a parabola ; 
To find the area of a field or lot, which is found to be 
the frustum or zone of a parabola, included by two 
parallel lines, and the intercepted curves of the para- 
bola 105 



CONTENTS. XI 

TKiaONOMETRICAL SURVEYINS. PAGK 

Mode of executing a trigonometrical survey 107 

JDetermination of the area of a triangle 109 

How to measure a tract of land by measuring a base line 
through it, and not departing from that line, and yet 
finding all the distances round the land, their course'^ 

and angles of the field, and the area :';> 

Correction of the difference of latitude and depai '.re m 

surveys taken with the compass 120 

To find what may be the error in the difi"erence oi rati- 
tude and departure of a given station arising from the 

inaccuracy of practice 121 

Table of errors in links and decimals ; Rules for altering 

the legs of stations in the correcting of surveys. . . . 124 
Description of an instrument by which any person, 
though unskilled in surveying, may measure a map, or 

part of a map, almost at one view 126 

Description and design of a new instrument by which 
distances can be found at once, without any calcula- 
tion 127 

The use of tlie instrument in measuring distances. . . . 132 

Example in measuring distance 133 

Given the bearings of any two stations of a survey, 
thence to determine the angle made by those stations . 136 

Method of calculation 141 

Another method of calculation wherein fewer figures are 

used 144 

A new and concise method of calculation, wherein fewer 
figures are used than in the common methods .... 146 

Noble's method of calculation 147 

Example in numbers 151 

To survey with the compass through any mine, or other 
cause for drawing the compass needle of its parallelism; 
Mean diurnal variation for every month in the year. . 153 



Xll CONTENTS. 

PAGE 

Manner of plotting the notes 155 

Lotting or laying out towns, etc 156 

Methods of keeping field-books 157 

Tracing of old mearings , 161 

Of levelling 163 

Field-book distances measured with a one hundred Ceet 

chain 165 

To lay out a road on a regular grade up a liill 166 

To inflect in curves on railrords and others 168 

Problems ITI 

To find the perpendicular ordinates from the chord G of 
any arc of a railroad, in order to set off the curve cor- 
rectly and speedily, without the help of an instrument. 173 
Tables of latitude and departure 180 

TABLES OF SURVEYS. 

The use of the foregoing tables in relation to surveys; 
Examples • 192 



SYSTEMS OP RECTANGULAR SURVEYING FOR SURVEYING THE 
PUBLIC LANDS OF THE UNITED STATES. 

Townships and sections ; What constitutes a range. . . 194 

Size of townships 195 

Establishment of standard parallels; Instruments to be 

used in surveying 196 

Measurement of township lines and subdivision lines; 

Tally pins; Process of chaining 197 

Levelling the chain and plumbing the pins 198 

Marking lines; Sight trees or line trees 199 

Marking trial or random lines 200 

Establishing corners; Points for perpetuating corners . 201 



Definition of and instructions for meandering; Meander 

corners 202 

Meandering of lakes, deep ponds and navigable bayous . 203 

Surveying ; Base line 204 

Principal meridian ; Standard parallels j Guide meridians. 205 

Exterior of township lines . , 206 

Index 209 



PRACTICAL SURVEYOR'S GUIDE. 

INTRODUCTION. 



The object of surveying consists in taking the 
measurements and observations of larger or smaller 
parts of the earth's surface, so that a map may be 
drawn of the part surveyed, and its content calcu- 
lated. A survey should include all the natural and 
artificial features of the ground, for instance, rivers, 
roads, railroads, fences, buildings, limits of cultiva- 
tion, boundaries of estates, etc. It is, however, 
not always necessary to take the measurement of 
all these objects, it depending mainly on the par- 
ticular object of the survey, which of them are to 
be included. Thus, for instance, in surveys for 
economical purposes, the quality of the soil and its 
producing capacity have to be taken into consider- 
ation, which is not necessary in topographical sur- 
veys. 

2 (17) 



18 THE surveyor's GUIDE. 

The *' points" which are to be determined in 
surveying are not the mathematical points treated 
of in geometry, but the corners of houses, fences, 
stones, etc., which are mere points in comparison 
with the extensive surfaces and areas which they 
are the means of determining. Strictly speaking, 
their centres should be regarded as the points 
alluded to. 

A straight line is determined^ that is, has its 
length and its position fixed, when the points at its 
extremities are determined ; and a plane surface 
has its form and dimensions determined, when the 
lines which bound it are determined. Consequently 
the determination of the relative position of points 
is all that is necessary for the principal objects of 
surveying, which are to make a map of any surface, 
such as a field, farm, etc. 

A map of a survey is a miniature copy of the 
field, farm, etc., as it would be seen by an eye 
moving over it ; or as it would appear, if, from 
every point of its irregular surface, plumb lines 
were dropped to a level surface under it, forming 
what is called in geometrical language its horizon- 
tal projection. 



INTRODUCTION. 10 

The scale, according to which the map is drawn, 
varies according to the object of the survey. Thus, 
for economical surveys it is tb-u-b to Wtjtt ; for city 
and village surveys about sh ; while for topograph- 
ical surveys it is considerably smaller. 



INSTRUMENTS FOR MEASURING 
DISTANCES, AND THEIR USE. 



A POINT in the field may be indicated either by 
a natural or artificial mark, the vertical corner of a 
building serving, for instance, for the former. Such 
corner of a building marks the points at which it inter- 
sects the ground. In the same manner a lightning 
rod or a vertical flag pole may determine a point. 

The mode of artificially marking a point in the 
field depends on the time the mark is to last. If it 
is to be permanent, as, for instance, the boundaries 
of estates, stones are used. The intersecting point 
of two lines cut in the head of the stone indicates the 
point in the field which is to be marked by the 
stone. Boundary stones must be set suflBciently 
deep in the ground to insure the permanency of 
their position. In taking measurements in cities, 
cast iron posts, planted perpendicularly in the 
ground, are frequently used. These posts are pro- 
vided on the top with a conical aperture for the in- 
(20) 



MEASURING DISTANCES. 21 

sertion of a marking pole, so that in measuring the 
point may be marked ieven at a greater distance. 
Temporary artificial marking may be effected by 
wooden pins. For temporary marking, whilst tak- 
ing measurements, painted marking poles shod with 
iron are used. If the distances are not very long, 
eight-feet poles, and for longer distances, 12-, and 
even 20- or 25-feet poles may be necessary, which 
then require rope-stays. The shorter poles are 
painted in alternate lengths of black and white, or 
red and white, the longer have the top painted and 
a red flag attached. 

A straight line in the field is established by 
two points marked in the above-described manner. 
The determination of further points in the straight 
line may, however, be effected in various ways and, 
hence, examples referring to definite cases will 
here be given. 

Let the points A and B, Fig. i, indicate a 
straight li7ie marked in the field hy two poles. To 
find the point lying in the prolongation of the 
straight line AB. 

Proceed with a marking pole to the neighborhood 
of the point C to be sought, and walk in a direction 



22 THE surveyor's guide. 

perpendicular to AB, until to the eye, looking in 

Q^LZZZIZ... Q-! O 

ABC 

Fig. 1. 

the direction of BA^A appears to be covered by 
the pole B. Then plant the marking pole, which 
had been taken along, so that it covers the poles A 
and B. The pole then marks a point C from A B. 
However, the poles possess a thickness, which must 
not be neglected, and hence the accurate execution 
of the operation is not as easy as it may appear 
from the above description. After planting the 
pole (7, step back a few paces and examine its posi- 
tion. 

From Fig. 2 it will be seen that an angular space 
PoF is hid from the eye at o, by the pole (7, this 
angular space being the greater, the nearer the eye 

p 

o e --^^h3s^ 

^ B C 

E' 

Fig. 2. 

IS to the pole. To the eye at o, the poles A and B 



MEASURING DISTANCES. 23 

appear simultaneously covered, as long as they lie 
in the angular space P o P, even if O is not exactly 
in the straight line AB. Hence, to reduce this 
angular space as much as possible, it is recommended 
to step back at least a few paces, in order to exam- 
ine whether the poles A^ B^ Care in a straight line. 
If the poles used have the same diameter, the 
position of the pole Q may also be tested by bring- 
ing the eye in such a position that now the right, 
and then the left edges of the poles A and C cover 
each other. If this is feasible, the pole C stands 
in the straight line AB ; because if C is not in a 
straight line as shown in Fig. 3, the pole B pre- 
vents the right edges of A and C from being cov- 
ered. 

a::zzz::z2zz::z:zD 

- ^ B c 

Fig. 3. 

The pole C is now said to be ranged in the direc- 
tion ABy or aligned in the straight line AB. 

Two points^ A and B, marked by poles, being 
given, to find a point C of the straight line AB, 
which lies between A and B. 



24 THE surveyok's guide. 

Place yourself a few steps behind B^ so that to 
the eye the pole A appears to be covered by B. 
Then by signals direct an assistant to shift the pole 
(7> held in a vertical position, in the direction oi AB 
until it is also covered by B. The pole then 
marks a point Q in the straight line AB. In this 
case it is also said the pole is ranged or aligned in 
the straight line AB. 

In order to maintain the pole (7 in a perpendicu- 
lar position, the assistant should grasp it above the 
middle, and hold it pendent between the thumb and 
index finger. The pole then assumes by itself a 
perpendicular position. 

It is, of course, necessary to explain to the assist- 
ant the meaning of the signals. He must further 
be instructed to constantly turn the face towards 
the surveyor, and hold the pole in a perpendicular 
position with the arm extended. 

As regards signals, the shifting of the pole to 
the right or left by the assistant is indicated by 
lifting the right or left arm. Making signs to the 
right or left for this purpose should be avoided, as 
they might be readily misunderstood, especially at 
a greater distance. At great distances, or with an 



MEASURING DISTANCES. 25 

unfavorable light, it is also advisable to hold a read- 
ily visible object, for instance, a pocket handker- 
chief, in the hand. To indicate to the assistant that 
the pole held by him is in the right position, move 
the hand up and down in a vertical direction. The 
assistant then plants the pole in the indicated place. 

The poles should be set truly vertical, and so 
fixed as to remain so. The loss of time in having 
to send men long distances to reset poles on windy 
days may be very great. The vertical position of 
a pole may be readily tested by a plumb line. 

The point C of the straight line A B, which lies 
between A and B^ may also be found without the 
help of an assistant as follows : 

First determine according to the directions given 
on p. 21, a point i> in the prolongation of AB (see 

A ^ 5 . ^ 

Fig 4. 

Fig. 4) and then the point in the prolongation 
from BB. 

How to determine a point in the straight line 
AB, when it is impossible to take position in the 
prolongation of AB. 



26 THE surveyor's guide. 

In fixing an intermediate point in the straight 
line AB according to the preceding methods, it was 
supposed that the surveyor could place himself in 
the prolongation of AB, for instance, behind B, 
and look towards A. This, however, is sometimes 
not possible if, for instance, the two points A and 
B are indicated, as in Fig. 5, by the corners of 




rig. 5. 

two buildings. The mode of procedure is then as 
follows : 

From any desired point aj, which should be 
located as near as possible to the straight line AB 
place a pole b^, in the straight line a^B. Next 
from 5i, place a pole, a^, in the direction of Ab^ 
Then again from a^, place a pole, b^, in the direc 
tion of a^B, and so on. The poles a^, b^, aa, h, con 
stantly come closer to the straight line AB. 

After a few repetitions of this operation, a point 
a or 5, lying in the straight line AB, will be 
reached. 



MEASURING DISTANCES. 27 

The above described process is also employed for 
determining an intermediate point, when the straight 
line AB passes over a hill, so that it is impossible 
to see B from A. The assistant must, however, 
be careful to select the points designated in Fig. 
5, bi, hi, etc., so that A is visible from them, and 
the points «i, otj, as, so that B can be seen from 
them. 

Points in the straight line AB may also be deter- 
mined if a building stands between A and B. 
Since, however, measurements of distances are re- 
quired for the purpose, the solution of this problem 
will be given later on. 

Length of a straight line AB. By the length 
of the straight line AB is understood the length of 
its horizontal projection, as for instance, the length 



Fig. 6. 

CB in Fig. 6. The length AB of the straight line 
connecting the points A and B, is called the ob- 
lique length. 



28 THE sueveyor's guide. 

The most important instruments for measuring 
distances are the measuring rods, the tape-measure 
and the chain. 

The measuring rods, of which at least two are 
required for measuring a distance, are wooden rods 
or bars, protected on their ends by metal, and se- 
cured against moisture by being several times satu- 
rated with hot oil. They are painted aud graduated 
to feet and tenths, the feet marked on it being, as 
a rule, alternately painted black and white. 

For measuring a horizontal straight line AB, 
two measuring rods are required. The rod bearer 
places one end of the first rod at A, and aligns it 
in the straight line AB. He then takes the sec- 
ond rod, carefully places it against the end of the 
first and also aligns it in the straight line. He then 
takes up the first rod and lays it against the end of 
the second in the direction of AB. The measure- 
ment is thus continued until one of the rods extends 
over the terminal point B of the line to be meas- 
ured. To guard as much as possible against errors 
in counting, each rod when taken up should be 
counted aloud. The distance of the point B from 
the end of the last rod but one, is then read off 



MEASURING DISTANCES. 



29 



from the graduation of the last rod. Now, sup- 
pose the measuring rods are each 20 feet long and 
the entire distance is 12 measuring rods and 3J 
feet, then the length of AB is (12 X 20 + SJ feet) 
= 2431 feet. 

IToiv to measure ivith the measuring-rods a line 
AB, ivhich is not liorizontal. 

As previously stated, by the length of AB is 
understood the length of the horizontal projection 
AB' of AB (Fig. 7). For taking the measure- 
ment of this length two persons are required. 




Fig. 7. 

One person, by the eye., and for very accurate 
measurements, with the assistance of the plumb 
line, sets a prismatic rod perpendicularly at the 
point A. The other person lays the measuring 
rod in a truly horizontal position, so that one end 



30 THE surveyor's GUIDE. 

touches the prismatic rod and the other the ground, 
and aligns it in the straight line AB. The first 
person then again plants the prismatic rod perpen- 
dicularly at hi, and the second person again lays 
the measuring rod horizontally on the prismatic 
rod and aligns it in the direction of AB, and so on. 
By now counting the number of lengths of measur- 
ing rods and measuring the horizontal distance of 
the terminal point b of the last measuring rod from 
B, the length of the line AB is found. 

The tape-measure and its appurtenances. The 
steel tape is from 25 to 100 feet or more in length 
J to f inch wide, and about yV i^ich thick. It is 
graduated to feet and tenths or twelfths. It is 
convenient for measurements made at any height 
from the ground, and also useful for long offsets. 
But its liability to twist and kink renders it easily 
broken, while few persons can anywhere be found 
to repair it. With care one may be safely used for 
a long time, but it should not be left, even for a 
moment, in inexperienced hands. Woven tapes 
strengthend with cords of catgut or wire are also 
used for the same purpose, but are far less accu- 
rate, and are unsuitable for measuring more than 



MEASURING DISTANCES. 31 

two tape-lengths in one continuous distance, without 
appreciable error. Common measuring tapes are 
altogether untrustworthy. They stretch to an ex- 
tent visible to the naked eye, and shrink after wet- 
ting. 

On the ends the tape is provided with stout metal 
rings, which serve for the reception of stakes. The 
latter are wooden rods 3 to 4 feet long, with a 
diameter somewhat smaller than that of the termi- 
nal rings of the tape. Their lower end is shod 
with iron, and provided with an iron cross pin. 
The object of the pin is a two-fold one : it prevents 
the ring of the tape from sliding off the stake, and 
serves for forcing the latter by means of the foot 
into the ground. 

To take measurements with the tape two per- 
sons are required, the forward and the hind man, 
each of them carrying one of the two stakes over 
which the terminal rings of the tape are pushed. 
The forward man. Walking in the direction of AB, 
pulls the tape along until the hind man arrives at 
A. The latter then draws the attention of the for- 
ward man to the fact by calling out " halt." The 
hind man now sets his stake at A^ and ranges the 



32 THE surveyor's guide. 

stake of the forward man in the direction of AB. 
The forward man, after noting the correct position 
of his stake, pulls the tape tight, so that it covers 
the point previously marked with the stake. The 
terminal point of the tape is then marked by the 
forward man by means of a marking or tally pin. 
The marking pins of stout steel wire are about 15 
inches long, and provided below with a point and 
above with an eye. At the commencement of 
measuring the forward man receives ten such mark- 
ing pins strung through the eyes on a wire ring. 
After marking the first length of the tape with one 
of the pins, he calls to the hind man " go on," The 
tape having become slack by the hind man taking up 
the stake, is again pulled forward by the forward 
man until the hind man notifies him, by calling 
out " halt," that he has arrived at the marking 
pin. The hind man then takes up the marking pin, 
replaces it by his stake, adjusts the stake of the 
forward men, and so on. This process is repeated 
until the forward man has passed the terminal 
point B of the line to be measured. The number 
of marking pins taken up by the hind man then 
gives the number of tape-lengths. By multiply- 



MEASURING DISTANCES. 33 

ing the number of marking pins thus taken up 
with the length (say 100 feet) of the tape, the dis- 
tance from A to the last marking pin is obtained. 
To this has to be added the distance from the last 
marking pin to B, which is read off from the tape 
itself, in order to obtain the entire length of AB. 

If the ten marking pins, with which tlie forward 
man sets out when commencing to take the meas- 
urement, do not suffice, those collected by the hind 
man in the course of measuring have to be delivered 
as often as necessary to the forward man. How- 
ever, to avoid mistakes, this should be done only 
after the hind man has taken up the tenth pin. An 
account of how often the ten marking pins have 
been delivered to the forward man must, of course, 
be kept by some convenient arrangement. 

Determination of the distance AB when meas- 
uring is prevented by an obstacle between A and 
B. 

This problem may be solved in various ways 
according to special conditions, and hence, a few 
solutions with reference to definite cases, will here 
be given. 



34 



THE SURVEYOR S GUIDE. 



To find the length AB when the straight line 
AB passes through a po7id or a forest. 

Choose a convenient point (Fig. 8) from 
which A and B can be seen, and the distances 




Fig. 8. 

measured. Mark the point (7 by a stake, extend 
the lines AC md BO beyond (7, measure ^(7 and 
BO, and make 

A,0 = Aa 

B,Q==BQ 
then 

AyB,=AB 



MBASUKING DISTANCES. 



35 



Hence it is only necessary to measure A^Bi. 
If, however, J-i^j are not accessible, make, in 
accordance with Fig. 9 or 10, 




then is 



A,0=~AO 
B,Q=~BQ 



A,B.^ ^AB 



and consequently 



AB = n A,B,. 



36 THE surveyor's guide. 

Hence it is only necessary to measure A2B2 and 
to multiply this line by n. 




Fig. 10. 

How to find the distance AB when the st7'aight 
line AB continues across a river. 

Fix first a point Q (Fig. 11) in the extension of 
AB; choose a convenient point Z), from which 
Jl, jB, C, can be seen, and measurements be taken 
toward B and Q. Measure BD and (7Z>, and 
make 

B,B=~BD 

n 

CD = --CD 



MEASURING DISTANCES. 



37 



then is Bid parallel to BQ, or, what is the same, 
to AB. Now determine the point of intersection 
Ai from AD, with the elongation of B^Ci, by sim^ 




Fig.n. 
uitaneously ranging a stake A^ in AB and BiO^. 
Then 

A,Bi = ^AB 

n 

consequently 

AB = n.AxBi. 
Hence to find AB it is only necessary to meas- 
ure AiBi^ and multiply by n. 



38 



THE SURVEYOR S GUIDE. 



Two points A and B are give'ri ; between A and 
B lies a forest. The direction of the straight 
connecting line of these poi7its is to be determined 
in A and B. 

The direction of AB (Fig. 12) may be estab- 
lished by determining on each side of the forest a 




point which lies in the straight line AB. If i) and 
E are such points, AB and 5 £' indicate the di- 
rections of the straight line ^^ in the points A 
and B. 

To obtain the points B and E^ choose laterally 
from AB a point C, which allows of looking and 



MEASURING DISTANCES. 



measuring towards A and B. Then measure A C 
and B C, and make 

A,0=-^AO 



then is 



B,0=^BO; 



A,B, =: —AB. 



Now, in two points (^ and e, so situated that they 
can be seen from C along the edge of the forest, 
set marking poles, and determine the points of in- 
tersection, Bi and Bi, of the lines Cd and Ce^ with 
AiBi. By then making 

OB=nCB^ 

OB==nCB,, 
B and ±J are two points of the straight line AB. 

Chains. These are made of various patterns, 
and are galvanized, painted or plain. The latter 
are most liable to rust, while the first are liable to 
be less correct from the additional process they 
undergo. The long-linked pattern, having each 
link a foot or a Gunter's link in length, is consid- 
ered advantageous, it being lighter with the same 
amount of similar material, and its form showing 
most readily any accidental kink or derangement 



40 THE surveyor's GUIDE. 

during chaining. Furthermore, its links can be 
readily hammered straight after being accidentally 
bent. The curb chain and such small-linked pat- 
terns are modifications introduced with the use of 
superior metal, the amount of which is correspond- 
ingly reduced. They can be made very light and 
convenient, but when damaged are less readily rec- 
tified than the old pattern. In any case, the 
length of a new chain should not only be tested 
with a good standard when simply laid straight, 
but also again after stretching it by a weight. 

During the progress of survey work, the length 
of the chain should be daily tested by comparison 
with a temporary standard marked for the purpose 
and kept invariable. Th» ordinary surveyor's 
chain is 66 feet, or four poles long, composed of 
100 links, each connected to the other by two 
rings, and furnished with tally-marks at the end of 
every ten links. The tallies should be read from 
the beginning to the end of the chain, and not- from 
both ends to the middle. 

Grumman'' s Patent Ohains. These chains, in- 
vented and patented by J. M. Grumman, of Brook- 
lyn, N. Y., are made of very light steel wire, the 



MEASURING DISTANCES. ' 41 

links being finely tempered and so formed at the 
ends as to fold together readily and thus dispense 
with the use of rings. 

Vara Chains. The Spanish or Mexican Vara, 
which is in general use in Texas, Mexico, Cuba and 
South America, is 33|^ inches long. The chains 
are made of ten or twenty varas, each vara being 
usually divided into five links, each link, including 
a ring at each end, is, therefore 6f inches. A 
chain of ten varas has titty links ; of twenty varas 
one hundred links. Each vara is marked by a 
round brass tally, numbered from one to nine in 
the ten-vara chain, and from one to ten, each way, 
in the twenty-vara chain. Sometimes, but rarely, 
the vara is divided into four links ; a ten-vara 
chain then has forty links, and a twenty-vara, 
eighty links. 

Met7'e Chains. The French metre is very gen- 
erally used as a standard in South America, the 
West Indies, etc. The number of links to a metre 
and the tallies are similar to those of the vara. 

Marking Pins. In chaining there are needed 
ten marking pins or chain stakes, made of iron, 
steel or brass wire, as may be preferred. The 



42 THE surveyor's guide. 

pins are about 14 inches long, pointed at one end, 
to enter the ground, and formed into a ring at the 
other, for convenience in handling. They are 
sometimes loaded with a little mass of lead around 
the lower end, so as to answer as a plumb when 
dropped to the ground, from the suspended end of 
the chain. 

In land measurement, the acre is the unit. It 
contains 4 roods, and a rood contains 40 perches. 
A perch is a square rod, otherwise called a pole. 
A rod is 5| yards or 161 feet. 

Hence,! acre =4 roods = 160 perches =4,840 
square yards = 43,560 square feet. 

One square mile = 5,280 X 5,280 feet = 640 
acres. 

Since the ordinary surveyor's chain is 66 feet 
long, a square chain contains 4,356 square feet, 
and, consequently, 10 square chains make one 
acre. Care should be taken not to confound 10 
square chains with 10 chains square. The former 
make one acre ; the latter space contains 10 acres. 

When the contents of a piece of land is given in 
square links, as is customary, cut off four figures 
on the right (i. e., divide by 10,000); to get it 



MEASURING DISTANCES. 43 

into square chains and decimal parts of a chain, cut 
off the right hand figure of the square chains, and 
the remaining figures will be acres. Multiply the 
remainder by 4, and the figure, if any, outside of 
the new decimal point will be roods. Multiply the 
remainder by 40, and the outside figures will be 
perches. The nearest round number is usually 
taken for the perches, fractions less than half a 
perch being disregarded. 
Thus— 

86.22 square chains = 8 acres, 2 roods, 20 perches; 

Also, 
64.1818 « =6 « 1 « 27 « 

Also, 
43.7564 " =z 4 " 1 '' 20 « 

Various methods of measuring distances. 
Wheel-pedometers record on a dial-face the num- 
ber of revolutions of, or distance passed over, by a 
wheel rolling on the surface of the ground. On 
very smooth and even ground the results are mod- 
erately fair, the error being chiefly due to slip- 
ping. 

Facing and pedometer. Next to guessing, 



44 THE surveyor's guide. 

simple pacing is the worst method of obtaining dis- 
tance, the inequality of the paces under various con- 
ditions, combined with the errors in counting, ren- 
dering it very inaccurate. A pedometer may be 
used to register the number of paces taken without 
any attention on the part of the person wearing it. 
It is made in the form of a watch, and carried in 
the pocket. The number of steps given by the 
pedometer, multiplied by the length of the step, 
will give approximately any distance walked over. 
In another form the instrument is intended to 
be regulated according to the length of the step 
of the person carrying it, and then the distance is 
registered on the dial in miles. The pacing 
adopted should be even, but natural, and not 
strained with the mistaken object of conforming to 
any arbitrary length, for instance, three feet. 
Some paced distance, on the level, up-hill and down- 
hill, should be tested by careful measurement to 
obtain the ratio for reduction to yards, feet or 
miles, under these three conditions of any future 
pacings. The ratio should again be frequently 
checked. It is also necessary to acquire the art 
of walking in a straight direction. To do this, fix 



MEASURING DISTANCES. 45 

the eye on two objects in the desired line, such as 
two trees, bushes, or stones, or tufts of grass. 
Walk forward, keeping the nearest of these objects 
steadily covering the other. Before getting up to 
the nearest object, choose a new one in line further 
ahead, and then proceed as before, and so on. 

Guessing or judging distance may, with con- 
tinued practice and checking, be carried to an 
accuracy that is surprising. The main points to be 
noticed are the rise or fall of the ground and the 
direction from which the light falls on any object 
at the distant point. Some persons estimate in 
yards, others in their own paces, which are more 
readily available for testing such guises. 



INSTRUMENTS FOR SETTING-OUT 

RIGHT ANGLES, AND 

THEIR USE. 



The simplest instrument for this purpose is the 
surveyor'' s cross, or cross staff. It consists of a 
block of hard grained wood, 3 or 4 inches square, 
and 1| to 2 inches thick, having two saw-cuts more 
than half through its thickness, and intersecting 
each other at right angles at the centre of the 
block. This block is fixed on a pointed staff, on 
which it can turn freely. 

Another form of the surveyor'' s cross (Fig. 13) 
consists of two pairs of sights (diopters) placed at 
the ends of two bars at right angles to each other. 
The slit, and the opening with a hair stretched 
from its top to its bottom, are respectively at the 
top of one sight and at the bottom of the opposite 
sight. The cross sits by means of a socket upon a 
pointed staff shod with iron. 
(46) 



SETTING-OUT RIGHT ANGLES. 



47 




Fig. 13. 

Another form of the surveyor's cross, the so- 
called cross staff head, is shown in Fig. 14. It is 
octagonal in shape. Four sides of the head are 
provided with sights (diopters), the oculars and 
objectives of which consist of slits (like A and _S), 
while upon each of the other four sides a slit CO' 
serves as the ocular, and a hair DD' as the objec- 
tive, the oculars and objectives upon the parallel 
sides belonging, of course, together. The visual 
planes AB, A'B', as well as OB and O'B' stand 
perpendicularly opposite to one another and inter- 
sect in the axis of the head, which is also the axis 
of the socket H and of the staff stuck in the latter. 



48 



THE SURVEYOR S GUIDE. 



With the assistance of either of the above de- 
scribed instruments the following problems may be 
solved : 




Fig. 14. 

1. To erect a perpendicular at the point C in the 
straight line AB. 

2. To let fall a perpendicular to a straight line 
AB from a point C. 

3. A straight line through the points AB is 



SETTING-OUT RIGHT ANGLES. 



49 



given. An intermediate point C in the straight 
line is to be found without entering the prolonga- 
tion of AB. 

How to erect a perpendicular at the point O in 
the straight line AB. 

It is supposed the point C (Fig. 15) has been 
found by ranging a stake in the direction AB. Set 

oD 



J 



Fig. 15. 

the instrument at C, and turn its head until the 
stake A is seen through the sight ab from b. By- 
no w setting a stake D in the visual plane of the 
other sight ed, then CD is perpendicular upon AB, 
because the visual planes of the two sights stand 
perpendicularly one upon the other. 

How to let fall a perpendicular to a straight 
line AB from a point C. 



50 



THE SURVEYOR'S GUIDE. 



First determine a point E in the prolongation of 
AB (Fig. 16). Then set up the instrument at a 
point of the straight line AB, which seems to the 
eye to be about the bottom of the perpendicular. 
Now turn the head of the instrument until B is 
seen through one of the sights, and note whether 
9i> 




W 



Fig. 16. 



the stake C is in the visual plane of the other sight. 
If such is the case, the staff of the instrument 
marks the bottom I) of the perpendicular CD. 
However, if C lies to the right or left of the visual 
plane, move the instrument to the right or left, and 
repeat the operation until the correct spot is found. 
How to determine an intermediate point in 
the straight line AB, 



SETTING-OUT RIGHT ANGLES. 51 

Set the instrument in what is supposed to be 
about the center of AB, and sight through the 
sight ab the point B. If the point chosen lies in the 
straight line AB at about C (Fig. 17), A can also 
be sighted from b, provided the position of the in- 
strument remains unchanged. If, on the other 






d_ 



g;^ ^B 



Fig. 17. 

hand, the point chosen lies outside the straight line 
AB at about 0^, then when sighting through ab 
from a to B, the line of sight from bi on, will pass 
A in the opposite direction, and the distance 
AAi, at which it passes A, will be about that of 
CCi, when C lies nearly in the centre of AB. 
Now, therefore^ move the instrument about half the 
distance of AAi, and repeat the operation until the 
back-sight covers A. 

To test whether the visual planes of the two 
sights Qdiopters) stand perpendicularly one upon 
the other. 



62 THE surveyor's guide. 

Suppose AB (Fig. 18) is a straight line marked 
by two stakes A and B^ and C an intermediate 
point in AB. Erect a perpendicular CD at the 
point Q. For this purpose sight through the sight 
ah the stake A^ and then set the stake D in the 
visual plane of the sight cd. The straight line 



(^ 



n 



Fig. 18. 

(7Z>i stands perpendicular upon AB only when the 
angle of the visual planes of the two sights is a 
right one. If it is not exactly a right angle, but 
as in Fig. 18, somewhat smaller, the angle ACD 
will also to the same extent be smaller than a right 
angle, because by the operation just described the 
angle aCd has actually been laid out at the point 
GmAB. 
By now turning the head of the instrument (see 



SETTING-OUT RIGHT ANGLES. 53 

Fig. 19) until the visual plane ah covers the stake 
Z>, and again setting in the visual plane of the 
other sight a stake E, then the angle BiCE is 
equal to the angle aCd^ and consequently the 

■OiTT-D 



6 
Fig. 19. 

angle A QE is double the angle of the visual planes 
of the two sights. Hence the instrument is correct 
only when A CE is an obtuse angle, A Q and E lie 
in a straight line, and the plane of sight ed covers, 
in the last position of the instrument, the point B. 
Surveyor's angle-mirror. This instrument 
(Fig. 20), consists of two mirrors. Si and Si, so 
placed as to form an angle of 45°. The mirrors 
are secured in a brass box closed towards the side 
of the vertex of the angle formed by them, and 
open on the other side. Above the mirrors the 



54 



THE surveyor's GUIDE. 



sides of the box are provided with rectangular 
apertures, the so-called windows Fx and F^. To 
the bottom plate G- is secured a handle which, as a 
rule, is provided with a small hook, to which a 
plumb bob may be suspended. 




Fig. 20. 

The construction of the angle-mirror is based 
upon the laws of the reflection of light by planft 
mirrors, which are as follows : 

1. The reflected ray lies in the plane determined 
by the axis of incidence and the incident ray. 

2. The angle of reflection is equal to the angle 
of incidence. 



SETTING-OUT RIGHT ANGLES. 65 

By the axis of incidence of a ray of light is 
understood the perpendicular upon the plane of the 
mirror at the point at which the ray of light strikes 
it ; and by the angle of incidence^ the angle which 
the incident rays form with the axis of incidence. 
By the angle of reflection is understood the angle 
which the reflected ray of light makes with the 
angle of incidence. 

The mode of operation of the angle-mirror will 
be explained by the scheme, Fig. 21, in which the 
two mirrors, S^ and ♦S'a are represented as simple 
lines in ground plan. 

Suppose, in the direction AB, a ray of light 
falls upon the mirror S-^. The axis of incidence 
for this ray is the perpendicular Bh in the point B 
upon the mirror Si. The angle of incidence is the 
angle ABh. If the ray AB is reflected towards 
BCy then the angle CBh is the angle of reflection. 
Now, as previously stated, according to the laws 
of reflection, the angle of reflection is equal to the 
angle of incidence, and hence, 

<CBb= <ABb. 
The ray BO now falls in the point (7 upon the 



66 



THE surveyor's GUIDE. 



mirror S2. The axis of incidence here is Cc, and 
the angle of incidence is BCc. If the ray is re- 
flected from the mirror 1S2 towards CD, then the 
angle DCc is the angle of reflection, and hence 
<DCc = <BOc. 




rig. 21. 



Thus, if a ray enters the angle-mirror in the direc 
tion AB, it passes out in the direction of CB 
Now, it can be demonstrated that the ray CD pasi 



SETTING-OUT RIGHT ANGLES. 57 

ing out stands perpendicularly upon the entering 
ray AB. 

If the point of intersection of the two axes of 
incidence be designated: U, then according to the 
proposition, " the outward angle of a triangle is 
equal to the sum of the inward opposite angles," 

1. <DOB=<OBO+<OOB 

= 2(a + ^). 

2. <cEB = <EBO+<EQB 

Erom this it follows that 

<B0B=2<eEB. 

However, according to the proposition, " two angles 
whose sides stand perpendicularly upon each other 
are equal," 

< CEB = < BSQ 
= 45°, 
consequently 

<i>O5 = 90°. 

Thus, the angle B OB, which the ray passing out 
forms with the entering ray, is constant; it is i'nde- 



58 



THE SURVEYOR S GUIDE, 



pendent of the angle of incidence A and of the ray 
AB. From this it follows that the direction of the 
ray passing out is not changed by turning the an- 
gle mirror around its axis. Therefore, the eye 
looking in the direction AB into the mirror, will 
see a quiescent picture, though the mirror may be 
turned around its axis. This property renders the 
angle-mirror very suitable for use, it requiring no 
support, it being simply held in the hand. 




Fig. 22. 

Use of the angle-mirror. By holding the angle- 
mirror before the eye vl, Fig. 22, so that both 
mirrors are vertical, and the eye on looking past 
the edge tj, of the mirror S^ through the window 
of the mirror *S'i, sees a stake P, while at the same 



SETTING-OUT EIGHT ANGLES. 59 

time it looks in the same direction into the mirror 
Si, the visual ray, according to the explanation pre- 
viously given, takes the course ABQD. If a 
stake stands in the straight line (7Z>, the eye A 
sees this stake in the mirror S^ at B. Hence the 
stake D appears to the eye at A exactly in the 
same direction as P. The stake P, seen directly, 
forms the straight continuation of the picture of the 
stake Z), which lies sideways. The point is the 
vertex of a right angle, whose sides pass throu^ 
the points B and 1). The angle-mirror is of such 
small dimensions that in the field it may be taken 
as a point ; hence, may be considered coinci- 
dent with the point obtained by plumbing the an- 
gle-mirror. If, therefore, a point P, seen through 
the mirror aS'^, lies perpendicularly over the pic- 
ture of another point Z> seen in the mirror S-^, the 
directions from the location of the mirror to these 
two points are perpendicular to one another. 

How to erect with the assistance of the angle- 
mirror a perpendicular to the 'straight line AB 
at a point Q in the latter. 

Place yourself before the point C (Fig. 23) 
with the face turned towards the side where the 



60 



THE surveyor's GUIDE. 



perpendicular is to be erected. Now hold the angle- 
mirror, with the open end turned towards A (or 
5), in a truly perpendicular position over C, and 
look with the eye for the picture of the stake A 
in the mirror. When this has been found, set the 



qG 



/d 



Fig. 23. 

stake P, so that when seen through the window of 
the angle-mirror, it is the direct continuation of A. 
Then AQD is a right angle and, hence, GB the 
desired perpendicular. 

]n order to be convinced at any moment that the 
angle-mirror is in the straight line AB^ it is recom- 
mended to previously range in the direction AB^ 
a stake E in the prolongation of AB. The angle- 
mirror is then in J.-S, when the pictures of the two 
stakes A and E cover one another. 

How to let fall with the assistance of the angle 



SETTING-OUT RIGHT ANGLES. 



61 



mirror a perpendicular CD from a point O to a 
straight line AB. 

Determine first a point E^ Fig. 24, in the pro- 
longation of the straight line AB. Then place 
yourself with the face towards A in the neighbor- 
hood of the bottom of the perpendicular sought, so 
that the eye is in the straight line AB^ which 




Fig. 24. 

is recognized by the two stakes A and E covering 
one another. Hold the angle -mirror close before 
the eye, with the opening turned towards (7, and 
note whether the picture of O appearing in the 
mirror is the straight continuation of the directly 
seen stake A. If such is the case, the position of 
the angle-mirror indicates the bottom of the perpen- 



62 



THE surveyor's GUIDE. 



dicular ; if not, walk back or forward in the straight 
line until the picture of is the continuation of A. 

How to find with the assistance of the angle- 
mirror an intermediate point C in the straight 
line AB. 

This operation is based on the following facts, 
which will be readily understood : 

If a perpendicular is first erected at (7, Fig. 25, 



Fig. 25. 

upon AQ^ and then one upon 5 (7, these perpendic- 
ulars coincide. If (7j is not a point in the straight 
line AB, but has the position indicated in Fig. 26, 
the two perpendiculars to AQ^ and ^Ci will devi- 
ate from each other, the two right angles AQJ) 
and BCiD\ being separated by an angular space, 
DxCiD'i. If now the point (7 occuDies the position 
indicated by C-i in Fig. 27, the perpendiculars to 



SETTING- OUT RIGHT ANGLES. 63 

AGi and BG% also do not cover one another, while 
the two right angles ACJ)i and BQJ)'^ partially 
cover one another. Hence, it will be seen that 



the surveyor is at a point C in AB only when the 
perpendiculars to J.C and BQ coincide, and fur- 




ther, that in order to reach the straight line AB^ 
he must walk forward if, as in Cj, the two right 
angles partially cover one another, or backward 



64 THE surveyor's guide. 

if the two right angles are separated by an angular 



Testing the angle-mirror as to its accuracy. 
The two mirrors of the instrument should form an 
angle of 45°. For the purpose of testing it, range 
in the given line AB marked by stakes, two stakes 
C and B, Fig. 28, and laterally plant a stake B in 
' -"'it the centre oi'CB. Now, with the assistance 



Fig. 28. 

of the angle-mirror, let fall a perpendicular to A, 
according to the directions previously given. This 
may be eflfected either by walking in the direction 
from B to 0, until the directly seen stake O is the 
straight continuation of the picture JS' seen in the 
mirror, or by walking in the direction from to B 
until the directly seen stake B forms the prolonga- 
tion of the picture of B. If the mirror is correct, 



SETTINa-OUT EIGHT ANGLES. 65 

the operator will both times strike the same point 
F. If, however, the angle of the two mirrors is 
not exactly 45°, he will first strike the point #1 and 
then the point F^. Both points F^ and F^ will lie 
at the same distance in opposite directions from 
the correct point F. (Fig. 28 illustrates a case in 
which the angle is smaller than 45°.) If, now, 
Fx and F^ have been found, the centre of the dis- 
tance FxFi is the bottom of the perpendicular 
sought. 




Fig. 29. 

Prism for right angles. This instrument (Fig. 
29) consists of a glass prism, the cross section of 
which is a right-angled isosceles triangle. The 
plane of the hypothenuse of the prism has a 
smooth reflecting surface. "The instrument is pro- 



G6 



THE SURVEYOR S GUIDE. 



vided with a handle, on the lower end of which is, 
as a rule, a hook or eye for suspending a plumb- 
bob. The prism serves as a substitute for the an- 
gle-mirror, and, generally speaking, is used in the 
same manner. It is smaller, so that it can be con- 




rig. 30. 



veniently carried in the pocket, and, being invaria- 
ble, does not require to be constantly tested. 

Use of the prism. By looking towards the 
stake P (Fig. 30), and holding the prism before 
the eye J., so that the axis of the prism stands 



SETTING-OUT EIGHT ANGLES. 67 

vertical, and the visual ray AB strikes tlie prism 
in the neighborhood of the sharp edge, and the 
plane of the hypothenuse stands about perpendicu- 
larly upon the visual ray, the latter in passing 
through the prism takes the course ABOD^F. 
Hence, a stake standing at F would appear to the 
eye A, looking through the prism, in the direction 
AP. Thus, while the eye looking over the frame 
of the prism sees the stake P, it perceives, in the 
straight continuation of the latter, the picture of 
the stake F in the prism. The angle POF is a 
right angle, and its vertex always lies so close to 
the prism, that in the field, the point obtained by 
plumbing the prism, may be designated 0. Hence, 
it may be said that the field-point obtained by 
•plumbing the prism is the vertex of a right angle, 
the sides of which pass through P and through F. 
If therefore, the stake P, which is directly seen, 
forms the straight continuation of the picture of 
the stake F, seen in the prism, then the visual 
rays from the position of the prism towards P and 
F stand perpendicularly one upon the other. 

To set out right angles with the tape measure 
alone. There are various methods for setting out 



68 



THE SURVEYOR S GUIDE. 



right angles with the tape measure alone ; two of 
them will here be given. 

Let AB he the straigJit line upon wliich at the 
point C a perpendicular is to be erected. 

1. Measure off equal distances CD and OE (¥ig. 
31) on each side of the point C. Then after fas- 
tening the ends of the tape with two pins at D and 
JE, grasp the tape in the centre, and walk sideways 
until both halves of the tape are stretched tight. 




2 D C JE P 

Fig. 31. 

The centre F of the tape then indicates a point of 
the perpendicular to be erected in C ; because the 
triangle DFE is an isosceles triangle, and in such 
a triangle the line connecting the summit with the 
centre of the base stands perpendicularly upon the 
latter. 

2. Measure off from C (Fig. 82), along the given 



SETTING-OUT RIGHT ANGLES. 69 

line a distance CD = 6 metres, then let two as- 
sistants hold in OD the ends of a portion of the 
tape, 18 metres long, grasp the tape at a point E 



A 



Fig. 32. 

at a distance of 8 metres from C and 10 metres 
from D, and draw it tight. CE is then perpendic- 
ular to A Bj because the triangle D CE is right- 
angled at E, since 

DW=W=100. 
and 

OF' + UE = 6' + 8' = 36 +64 = 100, 
consequently 

DE'= dW+ CE. 
In the following a few examples of the application 
of setting out right angles are given. 

1. Given, two points A and B, which are sepa- 
rated hyan obstacle which cannot he seen through. 



70 



THE surveyor's GUIDE. 



for instance, a forest. To determine their con- 
necting line in the points A and B, as well as the 
length of AB. 

Set out through the point A (Fig. 33) any con- 
venient straight line, which passes close by the 
forest, and determine upon it the bottom Q of the 




Fig 33. 

perpendicular let fall to it from the point B. By 
now measuring .4 (7 and BC, the length is obtained 
according to the Pythagorean proposition 

AB = ^AC'-i-BC 

To determine the direction of the straight line 
AB, erect upon A C two perpendiculars Avhich cut 
the straight line AB outside the forest. Now if 



SETTING-OUT RIGHT ANGLES. 71 

D and E are the bottoms of these perpendiculars 
and F and (r their still unknown points of intersec- 
tion with AB, it follows from the similarity of the 
triangles ABF and AOB that 

FB: BQ=AB'. AC. 



Consequently 



FB =^AB. 



AC 

From the similarity of the two triangles AECr 
and A OB, it further follows that 

as : BC=AE: AC, 

and therefore 

BO 
GE= jjyAE, 

By now measuring AB and AE, FB and GE 

can be calculated with the assistance of the two 
formulas. By now transferring the lengths thus 
calculated to the perpendiculars erected in B and 
E, the points F and Gr lying in AB are obtained. 
Bj AF the direction of the straight line at A is 
determined by BGr a.t B, and the problem solved. 
2. Criven, a straight line AB passing across 
a lake ; its length is to he determined. 



72 



THE SURVEYOR'S GUIDE. 



Erect in convenient points C and i^(Fig. 34) of 
the straight line AB perpendiculars and lay out 
upon them convenient, but equal lengths, GB and 
I'E. The connecting line BE oi the terminal 
points of these lengths is then parallel to AB, and 
in length equal to OF ; consequently 

AB = AC+BE^^FB, 




Hence it is only necessary to measure the three 
lengths J.(7, i>^, i^5; their sum total gives the 
length AB. 

3. A given straight line AB strikes in its pro- 
longation an obstacle, which cannot he seen 
through, for instance, a house; to find the pro- 
longation on the other side of this obstacle. 

Erect upon AB (Fig. 85) at B, a perpendicular 
BO oi such length that the line through parallel 



SETTING-OUT RIGHT ANGLES. 



73 



to AB passes the obstacle. Then erect at B upon 
D (7 a perpendicular QD of such length that a per- 




pendicular erected at I) upon CD passes the obsta- 
cle. Make the latter perpendicular DE equal 
BO ; then ^ is a point in the straight line AB, 
and the perpendicular ^i^ erected at EmponBU, 
the prolongation of AB sought. 




Fig. 36. 

4. A straight line AB is given. From a point 
C, a perpendicular is to he let fall to the straight 



74 



THE SURVEYOR'S GUIDE. 



line, the direct execution of the operation heing, 
however, rendered impossible by an intervening 
building. 

Erect at a convenient point I) m AB (Fig. 36) 
a perpendicular upon AB, and let fall to this per- 
pendicular from C the perpendicular CE. Now 
measure the distances CE and BE and make 
BF= CE. 

Then F is the bottom of the perpendicular sought, 
and BE its length. 

The problem maj also be solved as follows: 



("t 




Set out through C (Fig. 37) any convenient 
straight line and measure off upon it from C equal 
lengths CB and CE. From the points B and E 



SETTING-OUT* RIGHT" ANGLES. 75 

let fall perpendiculars to- the straight line AB. 
Suppose the bottoms of these perpendiculars are F 
and G ; then the centre ff of the length FCr is the 
bottom of the perpendicular sought, and the length 
of the perpendicular is 

C'ff=l{DF+ FG). 

To prevent inaccuracies, the erection of one per- 
pendicular upon another must in this method be 
avoided. 



SURVEY OF SMALLER TRACTS 
WITH THE ASSISTANCE OF 
THE PREVIOUSLY DE- 
^ SCRIBED INSTRU- . 

MENTS. 



To survey a three-sided field. 
A triangle being determined by the length of its 
sides, it is only necessary to measure the latter. 

c 




Fig. 38. 

A triangle may also be determined by its base 

AB (Fig. 38), its altitude CD, and the bottom I) 

of its altitude. Hence a three-sided field may be 

surveyed by determining with the assistance of the 

(76) 



SURVEY OF SMALLER TRACTS. 



77 



angle-mirror or the prism the bottom D of the 
perpendicular let fall from (7 to AB^ and then 
measuring with the chain, tape or rods, the lengths 
AB, AB and CB. 

To survey a many-sided field or polygo'ri. Di- 
vide the polygon (Fig. 89) by diagonals into tri- 
angles, and measure the three sides of each trian- 
gle. Since each triangle is determined by its 
sides, the polygon also is thereby determined. 




Fig. 



Another mode of surveying a polygon is as fol- 
lows : 

Mark out by several stakes a straight line ab 
(Fig. 40), the so-called base-line and axis of the 
abscissa, which cuts the polygon as nearly as pos- 
sible in the direction of its greatest dimension, and 



78 



THE SURVEYOR'S GUIDE. 



let fall to it perpendiculars from all angles of the 
polygon. A convenient angle of the polygon, for 
instance the point (7, is then determined, according 
to its position, by the length of the perpendicular 
CCi let fall from it to the base-line ah, and by the 
distance of the bottom Ci of the perpendicular from 




a convenient point, for instance A^, upon the base- 
line ah, which has been chosen as the initial point 
for taking the measurement. The distance A^d is 
called the abscissa of the point (7, and the length 
C(7i, the ordinate of point C. Hence, every angle 
of the polygon is determined by its abscissa and 
ordinate. The abscissa and ordinate taken together 
are called the coordinates of the point O. This 



SURVEY OF SMALLER TRACTS. 



79 



method of surveying is also called the coordinate 
or normal' method. 

Noting the results of the measurements. To 
note the results of the measurements, so that there 
cannot be any doubt about their meaning, make first 
a rough sketch of the tract to be surveyed, and in 
this sketch, mark the measurements found. The 
marking must be done according to a definite princi- 




ple, so that the position of the figures at once shows 
to which distances they refer. Write all measure- 
ments on the terminal points of the distances verti- 
cally to the distance to which they refer, so that, 
when looked at from the initial point of the dis- 
tance, they stand upright, i. e., can be read (see 
Fig. 41). The abscissas are measureed by adher- 
ing throughout to the same initial point, in Fig. 38, 



80 THE surveyor's GUIDE. 

they being, for instance, all counted from the point 
0. "The abscissa of the point VII. is 84.6 metres, 
i. e., the bottom of the perpendicular from the 
point VII. to the base line is at a distance of 84.6 
metres from ; the ordinate of the point VII. is 
35.8 metres, i. e., the length of the perpendicular 
from the point VII. to the basis is 35.8 metres. 

Athough the polygon is completely determined 
by its corner points, it is also advisable to measure 
the sides. These measurements are written in the 
sketch either perpendicularly to the sides, in the 
centre, or on the end of the sides, or parallel to 
the sides in the centre of the latter. 



PROBLEMS. 



Problem First. 
To reduce two pole chains and links to four pole 
ones. 

If the number of chains be even, the half of 
them will be four pole ones, to which annex the 
given links. Thus : 

1. In 16 chains, 37 links of two pole chains 
how many four pole ones : 

2)16. 37 



Ans. 8.37 

But if the number of chains be odd, take half 
of them and add 50 to the links. Thus : 
2)131.40 



Ans. 65.90 

Problem Second. 
To reduce four pole chains and links to two pole 
ones. Double the chains and annex the links if 
6 (81) 



82 THE surveyok's guide. 

they be less than 50, but if they exceed 50, add one 
to aouble the chains and take 50 from the links. 

C. L. 

Thus: 16.25 of four poles, how many two pole 
chains. 

16.25 

2 



Ans. 32.25 

C. L. 

2d. In 19.87 four pole chains how many two 

pole ones. 

19.87 
2.50 



Ans. 39. 37 

To reduce two pole chains and links to perches 
and decimal of a perch, multiply the chains by 

C. L. 

two and the links by four, thus: In 16.37 how 

many perches. 

16.37 
2. 4 



Ans. 33.48 

Article First — of Areas. 
A square is a plane figure having four equal 
sides and four right angles. To find the content, 



PROBLEMS. 



83 



multiply the side into itself and the product is the 
content. 

Example. 
Kequired the area of the square A B C D, one 
of whose sides is 25 chains 95 links. 



Fig. 42. 



25.95 
25.95 


A 

c 


A. R. P. 

67. 1. 14.44 


12975 
23355 
12975 
5190 


A. 67.34025 
4 


25.95 


R. 1.36100 
40 




P. 14,44000 





A parallelogram is a four sided figure whose 
opposite sides and angles are equal. To find the 
area multiply one of the sides by the perpendicular 
demitted from one of its opposite angles. 
Example. 

Required the area of the parallelogram A B 



84 THE surveyor's guide. 

C Dj the length of which is 15 chains, and height 
12 64. 



12.64 


A. R. p. 
18. 3, 33.6 





15 00 C 




12.64 
15 




6320 
1264 


Acres, 


18,960 
4 


Roods, 


3.840 
40 



Fig. 43. 



Perches, 33,600 

The content of an oblong piece of ground and 
cue side are frequently given to find the other. 
Divide the area in perches by the given side, gives 
the side required which is easily reduced into 
chains and links. 

If a lot contains 507 perches and is 14.25 long, 
what is its width. 



PROBLEMS. 85 



29)507 'l7.4827 
29 



8.25+12.06=8 37.0G 



217.0000 
203 

140 
116 

240 
232 

80 
58 

220 
203 

To draw maps of these figures is too obvious to 
require any explanation. 

5th. When the sides of the above figures are 
given in feet and inches, reduce the inches to deci- 
mal of a foot. Then multiply the length by the 
breadth and divide the product by 43-^60, the 
number of feet in an acre, the quotient will be the 
acres and decimal of an acre, which may be redu- 
ced to roods and perches by multiplying by 4 for 
the roods and 40 for the perches, pointing oif the 
proper number of decimal places each time, thus : 

A lot of land is 600 feet 4 inches long and 240 



86 



THE SURVEYOR S GUIDE. 



feet 3 inches wide, how many acres does it contain. 
600.333.X240.25=144230.00325 

Acres. A. R. P. 

This divided by 43560. gives 3.31106 or 3 1 09.T6 

4 



1.24424 
40 



9.76960 Ans. 

6th. A trapezium is a four sided figure the oppo 
site sides of which are neither equal nor parallel. 
To find the content, measure a diagonal and two 
perpendiculars to the opposite corners, multiply 
the diagonal by half the sum of the perpendicu- 
lars, and the product will be the area. 
Example. 

Let A B C D be any trapezium, having A C 80 
perches, and the perpendiculars as in the figure. 




Fig. 44. 



PROBLEMS. 



87 



25 
20 

2)45 

22.5 
80 

160)1800,0(li.l.00 An8. 
160 

200 
160 

40)40(1 
40 



7th. A triangle is a figure having three sides 
and three angles, any side may be called the base, 
having the base and perpendicular given. Multi- 
ply the base by half the perpendicular, or the base 
by the whole of the perpendicular, and take halt 
the sum. 

Example. 



Let A B C be any 
triangle whose base 
IS 100 two pole ch's 
and 15 links, and 
perpendicular 40 



Fig. 45. 




88 THE surveyor's guide. 

chains and 20 links, required the content m 

acres. 

100 15 
2 4 



40 20 200.6 perches and decimal. 

2 4 40.4 half the perpendicular. 



2)80 8 8024 

8024 

40 4 A. K. P. 

160)8104.24(50 2 24.24 A71S. 
800 

40)104 

80 

24 

8th. Having the three sid-es given to find the area 
rule, add the three sides together and take half 
the sum, from which subtract each side severally, 
multiply the half sum and three remainders con- 
tinually into each other, and the square root of 
the product will be the area. 

The most satisfactory proof of the above rule 
is the following: 

Let A B C be any triangle, B C its base, A B the 
greatest side, and A C the least, and let P be half 




PROBLEMS. »y 

the perimeter. In A B take A D=A C, joiii D 
and draw A E perpendicular to D C and E G pa- 
allel to B C cutting A B 
m G, with the centre G 
and radius G E describe 
a circle cutting A B in L 
and A B and E G pro- 
duced in K and H. Join 
H B and produce A E, 
H B till they meet in M. Since A D=A C and 
the angles at E are right, the squares of A E, 
E D are equal 2 A E,+2 E C and .-. E D=E C or 
D C=2 D E. Hence by similar triangles D G E, 
D B C, B C=2 G E=E H, and B C is also paral- 
lel to E H .-. H B M is parallel to C E D and 
(Euc. 1st 29th) the angle B M E=D E A, viz : a 
right angle, and H E being a diameter, M is a 
point in the circle. But from similar triangles 
D G E, D B C, D B=2 D G, to each of these 
equals add A D+A 0=2 A D, and B A+A C-2 
A G, to each of which equals add B 0=2 G E=2 
G K .-. A B+A 0+B 0=2 A K or A K is =P, 
half the perimeter. Now the area of the triangle 
A B 0=area A J) C+area B D 0=A EXD E+ 



90 THE surveyor's GUIDE. 

M EXD E (B M being parallel to D C)=A MXD 
E But by similar triangles A D E, A M B : A 
E : E D :: A M to M B, and by equi-multiples 
the first multiplied by third : the second multiplied 
by the third :: the second X by the third : the 
second X by the fourth. Hence, A EXA M : E 
DXA M :: E DXA M : E DXM B, i. e. the area 
of the triangle is a mean proportional between 
A EXA M, and E BXM B. Now E DXM B ,= 
P— A BXP— A C, and A EXA M-A LXA K= 
PXP — B C. Hence the area of the triangle is : 
^^TPXP— A BXP— A CXP— B C, which is the rule. 

Example. 
9th. Suppose the 
sides to be measur- 
ed by a four pole 
chain and be 

AB 10.64) 
A C 12. 28 y 
B C 9. 00 j 

Sum 31.92 




Fig. 47, 



I sum 15. 96 

5. 32 first remainder. 
3. 68 second do. 

6. 96 third do. 



PROBLEMS. 



91 



15.96X5.32X3.68X6.96=2174.71013216(46.()387 
16 

86)574 
516 



926)5871 
5556 

And since 

9323)31501 10 square 
27969 4 pole ch's 

make one 

93263)853232 acre, this 
279789 becomes 

ACRRS. 

932667)7344316 4.66337 
6528669 4 



2.65348 
40 

A R P 26.13920 

The content is 4 2 26. 

If the sides are in perches and decimal, divide 
the square root of the products of the half sum 
and three remainders by 160, and the quotient 
will be the acres, and the remainder divided by 40 
will be the roods. 

The same may be more readily done by loga- 
rithms, for as the addition of logarithms serves for 



92 THE surveyor's guide. 

the multiplication of their corresponding numbers, 
and that the number answering to the half of a lo- 
garithm will give the square root of the number of 
mat logarithm, it follows that half the sum of the 
logarithms of half the sum of the sides, and the 
three remainders will give the area, thus : 

Half sum, 15.96 log. 1.20303 

First remainder, 5.32 " 0.72591 

Second " 3.68 " 0.56585 

Tnird " 6.96 " 0.84261 



2)3.33740 

Square four poles 46.63 1.66870 

Or, 4.663 

4 

2.652 
40 

A. R. P. 

26.080 4 2 26 as before. 
10th. When the three sides are given and the 
angles are required, call either side on which the 
perpendicular will fall from the opposite angle the 
base, then as the base is to the sum of the other 
two sides so is the difference of those sides to the 
difference of the segments made by the perpen-. 
dicular, then half that difference added to half the 



PROBLEMS. 



93 



sum gives the greater, and substracted the less, by 

which means it is divided into two right angled 

triangles, the hypothenuse and one leg of each 

being given, the angles are easily found by plane 

trigonometry. 

Example. 
Let A B C be / \ ng. 48. 

any triangle hav- 
ing the sides giv- 
en as follows, viz; 
A B 88, B C 54 
and A C 108 to find the angles. 

A B=88 Then as 108 : 142 :: 34 
B C=54 34 




142 sum 
34 difference. 



568 
426 



108)4828.000(44.703 diff. of the 
432 segments at the base 

22.351 half diff. 

508 
432 

760 
756 



400 
324 



94 THE surveyor's guide. 

Then half the base 54+22.351=76.351, the 
greater segment A D, and 54—22.351=31.649 the 
less segment. 

The triangle is now divided into two right angled 

triangles, the hypothenuse and base in each being 

given to find the angles, as follows : 

As A B 88 1.944482T 

: Rad. 90° 10.0000000 

:: A D 76.351 1.8828147 



11.8828147 
i.9444827 



: Sine A B D 60°.ll' 9.9383320 

Ana 90— 60°.ll'=29°.49'.r-Angle BAD. In 
the same way C B D is found to be 35°. 53' its com- 
plement 54°.07"=/' B CD. 

Now A B D=60°.ll' 
B D=35 .53 



Angle A B C-- 


=96 


.04 


t 


A= 


29 


.49 


L 


C= 


54 


.07 



180 .00 Proof as the three angles 
of every plane triangle are equal to 180° per 32d 
of the 1st of Euclid. 

11th. Many things occur to the practical sur- 



PROBLEMS. 95 

veyor in the triangle, some of which I shall take 
notice of in this place. It often happens in prac- 
tice that the two sides and their included angle are 
given to find the other angles and side. 

KuLE. — As the sum of the sides is to their differ- 
ence so is the tangent of half the sum of the oppo- 
site angles to the tangent of half the difference ; 
this half difference added to half the sum of the 
angles at the base gives the greater, and sub- 
tracted the less. Then as sine of either of the 
base angles is to its opposite side, so is sine of the 
contained angle to the required side. 



A Example. 



Let AC 
=80, B C 



Fig. 49. 

110,and 




L A.QB 

102°.30'to 

find A B 

and the angles A and B. 

Side B 110 From 180 

Side AC 80 take /. C= 102.30 



Sum 190 2)77.30 sum of bas< 

angles. 

Diff. of sides 30 I sum =38.45 



96 



THE surveyor's GUIDE. 



Then as 190 log. 2.2787536 38°.45' 

: 30 " 1.4771213 7 .13 

:: Taff't 38°.45' 9.9044910 

45 .58 ^ A 

11.3816123 

2.2787536 31 .32 ^ B 



!:Tag'tof|difr.7°.13' 9.1028587 

Then as sine B 31°.32' 9.7184971 
: A C 80 1.9030900 

:: sine C 102.30 9.9895815 

Or its supplem't 77.30 

11.8926715 
9.7184971 

To A B 149.34 2.1741744 

12th. Again, it often happens that the area 
must be found from the foregoing data, in that 
case multiply the two sides together, and that pro- 
duct by the natural sine of ^ the contained angle, 
gives the area. 

Example. 



Fig. 50. 




Let ABC 
be a triangle 
having the 
side A C 13 
chains, A B t 
7c. 501. and /- B A C 42° to find the area. 



PROBLEMS. 9T 



7.5 
13 

225 
75 



^T.5X.384565 half the nat'l sine of 42<»= 

A. R. P. 

tJ2.SiJ square four pole chains = 32 19.2 An». 
Demonstration. 
Let fall the perpendicular B. D. 
A B : B D :: rad : sine A 
.-. B D=--A BXsine A 



Ead But rad.^1. 

,•■ B D=A B=sine. Multiply each side by 
A C ai.d B D. A C=A B. Sine A.XA C 
But A. C. B D— the area. Hence, 



2 
A B. A C. Sine A=area, which is the rule. 



13th. Let B A C be a triangular farm, and P a 
well of water. It is required to draw a line or 
fence from the well that will divide the farm 

equally between two partners : 

7 



98 



THE surveyor's GUIDE. 




E D 

Find D the middle of the base, B C, and from 
P take a course of P D. Again set your instrument 
at A, and take the same course A E ; cause a pole 
to be set at E, a line or fence from E to P will 
oisect the farm, which is easily demonstrated from 
the figure. See Bland. 

14th. Again, suppose the well P, to be situated 
within the farm, and it be required to divide it 
equally between three occupants, so that each may 
have the use of the well. a 

In fig. 52 di- 
vide the base B 

C, into three 

1 . • X/ / I '■ \\ Fig. 52. 

equal parts in 

D and E. Set 

your instrument 

at P, and take ^ 




PROBLEMS. 



99 



the courses P D and P E. Remove your instru- 
ment to A, and take A F the same course as P D, 
and A G the same as P E. Cause stakes to be driven 
at F and E in a straight line between B and C. 
Fences from F, G, and A, to P, trisect the farm, 
which is plain from the figure. 

15th. To find the area of a Trapezoid Rule, 
multiply half the sum of the parallel sides by the 
perpendicular distance between them, and the pro- 
duct is the area. 



Let figure 53 be a 
Trapezoid ; if A D be g v 
bisected in E, and E 
F drawn parallel to 

A B or C D, it also ! ij^ig.ss. 

bisects B C in F. — 
Through F draw G 
H parallel to A D. 
It is evident the triangles, B F G, and F C H, 
are similar and equal. (26th Euclid, 1st.) .-. E F, 
half the sum of the sides, multiplied by the per- 
pendicular distance between them, A D, gives 
the area. 



F 



100 



THE SURVEYOR S GUIDE. 



Being surveying on the side of a bog, and want- 
ing four acres to make up a division, and seeing A 

Fig. 54, 




A 50 

B would pass through a pond, I found A C fifty 
chains, and L C 56*^ ; how far must I measure 
from C towards B, so that the triangle ABC, 
may contain four acres. 

Since A C X C B X i the natl. sine of 56°=4 
acres, it follows that 4 acres divided by the pro- 
duct of one half the natl. sine of 56° into A C, 
gives B C the required side. Thus : 

50X4=200 perches X, 4145188=82.9 ; and 640 
perches in 4 acres, divided by 82.9=7.72 per the 
length of B C, and in like manner any other simi- 
lar case can be done. 

17th. Sometimes it is found necessary to ob- 
tain the area of a trapezium from having the 
diagonals and the angle of intersection given. 



PROBLEMS. 101 

Rule — Half the product of the diagonals multi- 
plied by the natural sine of the angle of intersec- 
tion, will be the area. 

Example. 
If the two diagonals of a trapezium be 40.15, 
and 60.13 chains the /- of intersection 75° 45', 
what is the area, i of 40.15X60.13=1207.1097= 
half the product of the diagonals, and 1207.1097X 
96923=(natural sine of 75°45')=1169.96693453l-- 

A. R. P. 

the area, in square four pole chains, or 116. 3. 39. 47. 
Answer. 

18th. To find the area of a trapezium, when 
each side and the angle of intersection of the 
diagonals are given. Mule — Square each side of 
the trapezium ; add together the squares ot each 
pair of opposite sides ; subtract the less from the 
greater; multiply the difference by the tangents 
of the angle of intersection. One fourth of the 
product will be the area. 

Example. 

What is the area of a trapezium, the sides of 
which are 10, 13, 7.16, 8.32, and 10.05 chains 
respectively, and the V of intersection of the 
diagonals 52° 15'. 



102 THE surveyor's GUIDE. 

(10.13)=102.6169 

^ 8.32)--= 69.2224 



171.8393=Sum of sqs. of opposite sidea 
(15.05)=226.5025 
( 7.16)= 51.2656 

277.7681=Sum of sqs. of other sides. 

105.9288 Difference, 
Multiplied by .32288=^ the natural tangent, 



34.20290944 or 



A 3. 1 .27,23 perches. 

For a demonstration of the foregoing, see Crib- 
(son's Surveying, hy Trotter. 

19th. To find the area of a trapezium, when the 
four sides are severally given, and also the sum 
of any two opposite angles. Rule — From half the 
sum of the four given sides, subtract each seve- 
rally ; multiply the four remainders continually 
together ; from the result subtract one half the 
continual product of the four sides, multiplied by 
unity, increased by the natural cosine of the sum 
of the given angles. The square root of the 
result will be the area. 



PROBLEMS. 103 

Remark. 

In the application of this theorem, it must be 
carefully remembered that the cosine uf an angle 
is positive when that angle is in either the first or 
fourth quadrants, and negative when it is in the 
second or third quadrants. For a demonstration 
of this beautiful theorem, see also, Grihson, by 
Trotter. 

N. B. When the sum of the opposite angles is 
180°, that is, when the trapezium can be inscribed 
in a circle, the above rule is simply : from half the 
sum of the given sides, subtract each side seve- 
rally ; multiply the four remainders continually 
together, and extract the square root, gives the 
area. 

Example. 

" One morning in May I went to survey. 

As soon as bright Sol I espied ; 

I measured round a four cornered ground. 

In the margin see the length of each side ; 

The angle at B, together with D, 

An hundred and fifty degrees ; 

The meadow's content is all that I want, 

Assist me kind youths, if you please." 



104 



THE SURVEYOR'S GUIDE. 



A B 15.60 
B C 13.20 
C D 10.00 
D A 26.00 ch'ns. 



2)64.80 sum. 



32.4=1 sum. 




Fig. 55. 



16.80=lst remr. S=half the sum. 

19.20=2d do. of the sides. 

22.40=3d do. 
6.40=4th do. 

Whence (s-A B)X(s-B C)X(s-C D)X(s-D A)- 
32.4X16.8X19.2X22.4X6.4=46242.2016=46242. 
2016 
And A B. B C. C D. D A.X(l+cos. 150°) 



That is 15.60X13.20X10.00X26.00 



-X0.1339746=3586.44C4 



DifFerence=42655.7552 
The square root of 42655.7552 is 206, 5327= 

A. R. P. 

area in square four pole chains, or 20. 2. 24,55232. 

N. B. This problem is taken from Deighan's 

Arithmetic, vol. second, page 148, and the answer 

A. R. p. 
there given is 21. 2. 00,64, which is obtained by 

taking the trapezium to be inscribed in a circle, 

which is not the case. 



PROBLEMS. 105 

When the opposite angles of a quadralateral are 
equal to two right angles, a circle can be descriljed 
about it. The rule to find the area, then, is : mul- 
tiply the half sum, and four remainders continually 
together, and extract the square root, for in that 
case l+cos.(A+B)=0. 

21st. To find the area of a circle having the 
diameter given. Rule — Square the diameter, and 
multiply by .7854, and you have the area. 

22d. To find the area of an ellipsis. Rule — 
Multiply the transverse and conjugate diameters 
together, and that product by .7854, and you have 
the area. 

23d. To find the area of a parabola. Rule — 
Multiply the height by the breadth, and take two- 
thirds of the product ; you have the area. 

24th. To find the area of a segment of a para- 
bola. Rule — Multiply the base of the segment by 
the altitude thereof, and two-thirds of the product 
gives the area. 

25th. To find the area of a field or lot, which is 
found to be the frustum or zone of a parabola, 
included by two parallel right lines, and the inter- 
cepted curves of the parabola. Rule — Add the two 



106 THE surveyor's GUIDE. 

parallel ends, divide the square of either of these 
ends by this sum, add the quotient to the other 
end, multiply this sum by the altitude of the frus- 
tum or distance of the ends, take two-thirds of the 
product, and it gives the area. 



TRIGONOMETRIGAL SimYEYlNG, 



26th. It was not my intention to say any thing 
concerning this branch of surveying, as it is too 
extensive a subject for this small work ; but as 
some young readers may not have met with any 
thing on that subject, I will present them with an 
outline of how that grand operation is conducted. 

When an entire country, or part of a country, 
containing one or more counties is to be surveyed, 
it is done by triangulation, and the application of 
the rule given in the 12th section of this work. A 
line of some miles in length is measured and re- 
measured in order to prove its accuracy, on some 
plane or heath which is nearly level, first havmg 
been traced by a transit instrument, and poles 
placed in an exact straight line, to guide the meas- 
urers, as A B in the annexed figure, which is assu- 
med as the base of the operations. A number of 
hills and elevated spots are selected, on which sig- 
nals can be placed, suitably distant and visible 
(107) 



108 



THE SURVEYOR S GUIDE. 



one from another. Thus, ifACDEBHG 
F, &c., be several objects, the situations of which 




are to be laid down on a map, and they are 
within the lines, ACDEBHGF, accu- 
rately Calculated. It is supposed that the stations 
A and B are chosen such as that all the others can 
be seen from each of them. Then from the ex- 
tremity A, measure the angles E A B, D A B, 
CAB, &c., H A B, G A B, F A B, &c. And 
from the other extremity B, measure the angles, 
C B A, D B A, E B A, &c., F B A, G B A, H B A, 
&c. And as the common base, A B, and the seve- 
ral angles of all the triangles are now known, the 
sides, A C, A D, A E, &c. may be determined by 
simple proportion, for as the natural sine of 



TRIGONOMETRICAL SURVEYING. 109 

ACB:AB::sineC AB: C B andso issine ABC 
to C A, and so through all the triangles, the three 
sides being thus found in each triangle, the area is 
easily found, as shown in section 8th of this trea- 
tise. But to insure accuracy the objects C D E, etc., 
should be all intersected from some third station, 
O in the base A B, otherwise the figure may ap- 
pear in the plotting to be right when it is not so, 
and there will be no means of knowing whether 
the angles have been correctly taken without going 
over the work again. 

27th. Here follows an example of a triangle con- 
A. K. p. 
taining a mean area of 1135.2.12.79. The sides 

of which were traced by a transit instrument, and 

poles placed at the several points marked thus ; 

this being done, the respective distances of the 

sides were ascertained by a mean of measures as 

follows, viz : 

B A 14643 links, or 9664.38 feet, A C 17814 
links, or 11777.24 feet, B C 16588 links, or 10948. 
08 feet. The angles were taken by a theodolite 
as they are marked in the figure. 

Now to determine the area of the triangle, A 
BO: 



110 



THE surveyor's GUIDE. 




14643 links, or 9664.38 feet. 

1st. From the data, A B, and the three angles of. 

the known formula 

A B^Xsine BXsine A, a r. p 
=1135.2.27.18 



2 sine C. 
2d, by B C, and the three angles, 

the area will be 1135.3.029 

3d, by C A, and the three angles, 

the area will be 1135.0.38.6 



TRIGONOMETRICAL SURVEYING. Ill 

dth, by data A B, and the two 
adjacent angles, we have by the 
known formula, 

A B^Xsine BXsine A, 



2 sine (B+A) 
The area will be 


A. R. V 

1135.2.25.7 


5th, and by B C, and the two ad- 




jacent angles 

6th, by a similar formula from A 


1135.3.01.9 


C, and the two adjacent angles, 




the area will be 


1135.0.37.99 


7th, by data A B, and the adja- 




cent angle A, and the remote an- 




gle C, we have by the known 




formula, 




(A B)^X8ine AXsine (C+A) 





2 sine C area, 1135.2.27.8 

8th, by a similar formula from hav- 
ing A B, and the angles, B and 
C ; area 1135.2 28.2 

9th, by having C B and the angles, 

C and A; area 1135.3.03.58 

10th, by having C B and the angles 

Band A; area 1135.3.04.38 



112 . THE surveyor's GUIDE. 

11th, by a similar formula data C 
A, and the angles, C and B, gives 
the area 1135.0.39.66 

12th, by a similar formula from da- 
ta C A, and the angles A and 
B; area 1135.1.00.12 

13th, by data A BXB C, and the 
contained angle, we have 

A BXB CXsine B=1135.2.35.06 



2 

14th, by A CXA B, and the con- 
tained angle 1135.1.32.92 

15th, by A CXB C, and their con- 
tained angle C 1135.2.00.79 

16th, by data, A BXB C, and the 
angle, A, we have by a known 
formula, B AXsine A 



BC. 
-sine C, and A BXB C, sine (A+C) 



2 area 1135.2.394 

17th, by the application of similar 
formula to the data, A BXB C, 
and angle, C ; area 1135.2.30.4 



TRIGONOMETRICAL SURVEYING. 118 

18th, by A CXC B,and angle, A, 1136-0.19.51 
19th, by A CXB C, and angle, B, 

the area will be 1135.0.19.89 

20th, by A CXB A, and angle, B, 

the area will be 1135.1.10.5 

21st, by A CXB A, and angle, C, 

the area will be 1135.3.05.16 

22d, by the usual rule from the 

three sides, s. s — a. s — b. s — c. 1135.2.14.7 

Now the various data exhibited in this triangle 
have been ascertained with the same relative de- 
gree of precision ; and the different areas deduced 
therefrom have been subjected to the same loga- 
rithmic process, till the figure has been exhausted ; 
there is no reason to suppose that any one of them 
is nearer to the truth than another ; and taking a 

A. R. p. 

mean of the results we have 1135.2.12.97 for the 
nearest approximation to the true area. 

But suppose we consider the triangle as spheri- 
cal, and the admeasurement of the sides as the 
lengths of three arcs of three great circles of the 
sphere ; and, according to Sir Isaac Newton, the 
diameter of the earth to be 41,798,177 feet, we 
will then have, as the circumference of a great 



114 THE surveyor's GUIDE. 

circle of the earth is to 360°, so is the length of 

C B to the number of degrees or minutes, &c.; 

contained in the arch, C B, viz : 

As 131312964.37: 360°: 
And do. : do. : 

And do. : do. : 



11757.24 : l'.56".03868=arch C A. 
9664.38 : l'.35".38309= " AB 
10948.08 : l'.48".05263= " B C. 



Now let b a c, represent the sides of any spheri- 
oal triangle, and e the spherical excess, we have hy 
Lhuiller's theorem. Tangent ^ E= 

Tan. a+b+c. tan. a+b — c. tan. a — b+c. tan. — a+b+c. 

4 4 4 4 

And by restoring to a b and c, their deter- 
mined values, we find 

a+b+c=0° .1' .19". 8686 

4 

a+b— 0-0° .0' .32" .1771 
a— bj-c=0° .0' .21" .8493 

4 

And, — a+b+c=0° .0' .25" .8423 



Whence the log. tangt. of 0° .1' .19" .8686=: 6.5879531 

of .0' .32" .1771= 6.1931205 

of .0' .21" .8493= 6.0250065 

of .0' .25" .8423= 6.0979010 



2)24.9039811 



Log. of i the spherical excess= 2.4519905 
The arc corresponding to this log. will be found 



TRIGONOMETRICAL SURVEYING. 115 

to be ,00584 parts of a second, consequently the 
spherical excess is 02336 of a second, and by a 
well known theorem, As 180° : the area of one- 
quarter the surface of the sphere : : the spherical 
excess to the area of the spherical triangle, viz : 

As 180° 31500428420,3 the area of a great cir- 
cle of the earth in statute acres : : 023360 to 

A. R. p. 
1135.2.11.3 being | perch less than the mean 

area, which is in defect, but should be in excess ; 
but this is accounted for by the hills on the land 
not being taken into account ; the difference, how- 
ever, is insignificant, and shows that the diflference 
between a plane and spherical triangle of conside- 
rable dimensions is very inconsiderable. See Gib- 
son s Surveying hy Trotter. 

28th. How to measure a tract of land by measu- 
ring a base line through it, and not departing from 
that line, and yet finding all the distances round 
the land, their courses, and angles of the field, and 
the area, never before published. 

In order to do this expeditiously, the surveyor 
should be provided with an instrument having two 
telescopes, one of which is movable, and the other 
fixed, by which he can at any time take half a right 



116 THE surveyor's GUIDE. 

angipj from the base line, and also a right angle ; 
he must also have an active assistant with a flag- 
staff, to hold at the corners as he proceeds with the 
measurement on the base line. Let ABODE 
T M G H A be any tract of land that is to be sur- 
veyed, let the base K L, be traced through it 
with a transit instrument, and poles set perpen- 
dicularly, to be visible from one to another. Set 
your instrument at L, on the base line, which in 
this survey bears N 40 E. A theodolite and com- 
pass attached is the best instrument for this 
method ; adjust your instrument, and let L be the 
point where 45° inflected from the base L K wiU 
cut the flag-staff; at the corner H, commence 
chaining towards K, and five chains you find 45° 
degrees deflected from the base line to the flag- 
staff at B, on the left, will bisect it, which note in 
your field-book by an oblique line to the left, ma- 
king an angle as near 45° as the eye can judge ; at 
9.30 half a right angle to the right will cut a pole 
at G, and at 12.00 came the fence ; at 13.20 half 

0. L. 

a right angle will cut C, and at 19.15 you find a 

right angle will intersect H. Now it is evident 

c. L. 
that you are 19.15 distant from H, for H 19.15. L 



TRIGONOMETRICAL SURVEYING. 



117 



is an isosceles triangle, and .*. you mark 19.15 on 
the perpendicular. The next perpendicular is at 




^J5.oo /-$■• 



20, and the half right angle having been taken ar 

0. 

5 on the chain line, 20 — 5=15=the distance to B. 

c. L. 
Again at 32.35 you find half a right angle bisects 



118 THE surveyor's GUIDE. 

^he pole at D, and at 33.20 a right angle inter- 

c. L. 
sects at G, and 33.20— 9.30=80.40=the length of 

the perpendicular which set on it. At 34.20 you 
find the next perpendicular on the left to 0, and 
the one-half right angle having been taken at 13. 
20 .-. 34.20—13.20=21.00 the distance to C ; pro- 
ceeding in this way you have 43.35 — 32.35=11 
chains to D, and 51.30— 35,40=15.40=the dis- 
tance to M, and 57.40—38.30=19.10 to F, and 
60— 57.40=2.10=the perpendicular of the last A 
within the fence on the right and 62.30—60=2.30== 
the perpendicular without the fence ; also, 62.30 — 
41=21. 30=the distance to E, which A is to be 
ducted out of the area of the last trapezoid on the 
left. Thus you have found with very little trouble 
all the requisites for calculating ihe area of the 
land, and it may be remarked, that you might have 
commenced at the corner B and noted where the 
two perpendiculars fell at 19.15 and 20 and as you 
proceeded on your base line take back sights at 
the proper distances to intersect the poles at B and 
H, and the distances from where the perpendicu- 
h-^rs would fall to these several points would be the 
chains and links to be placed thereon. The dis- 



TRIGONOMETRICAL SURVEYING. 119 

tances all round the land, can be accurately found, 
for in the present case -/(A a^)+(a H-)= A II, 
and r G, and r H being given V(r G'')-f(r H^)=H G 
and so on all round the land, and seeing that the 
courses of A a and a H are given, the course of A 
H may be readily found, for having the distance 
and difference of latitude and departure, the course 
is given in the tables ; also, the internal angles 
can be easily found, for in the ^ A a H A a : 
Had. : : a H : tang't a A H, and so with the A 
B b A. Hence, the angle B A H, is known, and 
it is evident the same holds good all round the 
land, the bases and perpendiculars of all the 
right angled triangles being found from the base 
line and can be marked on the sketch as the sur- 
veyor proceeds. The same may be done with a 
good compass, for having the course of the base 
line, the courses of the normals to right and kft 
are known, and the course of J a right angle beiug 
once ascertained on the right and left of the base 
will always serve to find the points on the base 
where they are to be taken ; but this would require 
many trials and waste time, whereas, an instru- 
ment showing i a right angle will save much time. 



120 THE surveyor's GUIDE. 

Thus, in a plane country, the scientific reader will 
acknowledge the plan completely available, and 
the surveyor can calculate the content of the land 
on the margin of his book while his needle is set- 
tling, and be able to answer the farmer satisfac- 
torily, who thinks a surveyor should be able to tell 
the content the moment he has the last distance 
measured. 

The plotting and calculation of a survey taken 
on the above plan is so obvious as to require no 
explanation, seeing all the figures are either right 
angled triangles or trapezoids, to find the area of 
which is shown in figure 63. 

29th. The most correct method of correcting 
the difference of latitude and departure in surveys 
taken with the compass, to fit them for calculation, 
some authors divide the differences proportionally 
"among all the stations ; but as there may be some 
stations in a survey really correct, any alteration 
in them would make them incorrect, so that the 
altering of the legs of stations in surveys where 
land is of great value, is a matter of considerable 
importance. 



TRIGOJlOxMETRICAL SURVEYING. 



121 



Fig 59. 



Problem. 

Vo find what may be the error in the difference of latitude 
and departure of a given station arising from the inacu- 
racy of practice : 

Let the right angled triangle A B D, fig. 59, 
represent a station with its diiFerence of latitude 
and departure; if the angle A be the bearing, then 
will the leg A D, be the difference of latitude, and 
the leg B D, the departure ; but if the angle at B 
be the bearing, then will the leg B D, be the differ- 
ence of latitude, and D A the departure. Let the 
small angle B A b represent the error committed 
in taking the bearing, which may amount TJ min- 
utes, and the small part B e or E b, the error com- 
mitted in chaining, in proportion to the whole line 
A B, or A e, as 0,5 is to 5.00, (for in measuring the 



122 THE surveyor's guide, 

lengtn of lines, there may be an error committed 
of half a link in 10 chains ; (this is found by expe- 
rience), and let e a, b d, and E c be drawn parallel 
to B D, and B n o, and res, parallel to D A. 

Case 1st. Suppose A B to be the true bearing 
and length of a station, and A b the one found by 
observation. Now it is plain that instead of the 
triangle A B D, we shall have by observation the 
triangle A b d, so that there is an error of the 
(quantity n b, by which the leg B D is increased, 
and an error of the quantity B n, by which the leg 
A D is decreased, and the contrary may be sup- 
posed, if A b be the true distance and bearing and 
A B that found by observation ; but when the 
angle at A is very small, D d may be supposed 
equal to (0). 

Case 2d. Suppose the true length and bearing 
of a station to be A e, and that found by measur- 
ment to be A B the bearing exact. Now it is 
plain that the leg e a is increased by the error 
r B, and that the leg A a, is increased by the error 
r e or a D, and the quantities or errors by which 
each leg is increased are in proportion to the legs 



TRIGONOMETKICAL SURVEYING. 123 

themselves, that is, B r : e a : : r e : A a, and as 
B e is to A e. 

Case 3dt. Suppose A e the true bearing and 
length of a station, and A b the same, found by 
observation. This supposes a compound error both 
in chaining and bearing, and that the error in the 
bearing increases the smallest angle in respect of 
the bearing and its complement. Here we see 
that when the leg A a is increased to A D by the 
error in chaining, as in the last case, it shall, at the 
same time, be brought back to A d by the error in 
the bearing, as in case 1st. Therefore, the leg A a 
will be increased by the quantity r e — B n, or de- 
creased by the quantity B n — r e ; but r e is 
greater than B n, when the angle at A is small ; 
and B n is greater than r e, when the angle is 
near 45°; for they become equal when the angle, 
is about 25°; but at the same time the leg e a will 
be increased to d b, by the error b S=b n+B r. 

Case 4:th. Suppose A E the true distance and 
bearing, and A B that found by observation ; this 
supposes the error in the bearing to decrease the 
smallest angle. Now it is evident that the longer 
leg A c is increased by the error B o or D c, and 



124 



THE SURVEYOR S GUIDE. 



the shorter leg decreased by the error E o. But 
B o=B n+r e (for r e=n o) and E o=b n- -B r. 
These errors are easily found in numbers by con- 
sidering the figure, and that they are always pro- 
portional to the length of the stations. 

Here follows a table of errors in links and deci- 
mals, calculated for a station of 30 two pole 
chains, and for the different angles and their com- 
plements, under which they are placed, but which 
can be changed to any other length, by altering 
them in the same proportion as are the stations. 



B A b=4°error 
in bearing. 


2 

88 

3.2 
0.0 


12 

78 


23 
67 


3°2 

58 


42 

48 


45 


B e 1.6 links error in chain- 
ing. 


b n= 
Bn= 


3.1 

0.7 


3.0 
1.4 


2.8 
1.7 


2.4 
2.2 

1.0 
1.1 


2.3 
2.3 

1.0 
1.0 


Error in short Leg. ) Case 
Error in long Leg. J 1st. 


Br= 

r e= 


0.0 
1.5 


0.3 
1.5 


0.6 
1.4 


.^8 
1.3 


Error in short Leg. ) Case 
Error in long Leg. J 2d. 


bs=(bn+Br) 
ad=(B nj"r e) 


3.2 
1.5 


3.4 
0.8 


3.6 
0.0 


3.6 
0.4 


3.4 
1.1 


3.3 
1.3 


Error in short Leg. ] Cixse 
Error in long Leg. J 3d. 


Eo-^(br.-B r) 3.2 
Bo=(Bu-t-re) 1.5 


2.8 
2.2 


2.4 
2.8 


2.0 
3.0 


1.4 
3.3 


1.3 
3.3 


Error in short Leg. ( Case 
Error in long Leg. j 4th. 



CORROLLARY. 
Hence we may adopt the following rules for 
altering the legs of stations in the correcting of 
surveys : 



trigonometrical surveying. 125 

Rule First. 
When the course, or angle, is either great or 
small ; or when the difference of latitude and de- 
parture are found in the beginning of the tables, 
then the shortest leg may be increased or decreav«ed 
by any quantity not greater than 3.2 links, and 
the longest leg increased by any quantity not 
greater than 1.5 links. 

Rule Second. 

When the latitude and departure are found about 
the middle of the tables, or when the angle is 
about 20° under or over 45°, then the shortest 
leg may be increased by any quantity not greater 
than 3.6, or rather 4 links, and the longest leg 
left unaltered, which is, when the error in the 
bearing increases the angle opposite the smallest 
side ; but when contrary, the longer leg may be 
increased by any quantity not greater than 3 
links, and the shorter leg decreased by 2 links. 
Rule Third. 

When the difference of latitude and departure 
are found in the latter part of the tables, or when 
the bearing is about 45°, then either of the legs 



126 THE surveyor's guide. 

(they being nearly equal) may be increased or de- 
creased by any quantity not greater than 3 links, 
and the other leg by 1.4 links, but when one leg is 
increased the other must be decreased. 

These rules are on the supposition that the 
chaining is always too long, which, in practice, I 
have nearly always found to be the case ; but when 
a surveyor has reason to think otherwise, he may 
alter the rules to his opinion, not only in respect 
to this, but also relative to the quantity of the 
errors. 

A description of an instrument by which any person, though 
unskilled in surveying, may measure a map, or part of a 
map, almost at one view : 

Get a piece of good glass about 8 or 9 inches 
long, and 6 or 7 inches broad, and divide it into 
small oblong rectangles of eight-tenths of an inch 
by 5 five-tenths, as fig. 60th. By laying this in- 
strument (which I call a computor) on a map you 
can tell with very few figures, sometimes with the 
eye only, how many of the rectangles are con- 
tained in the map, and consequently, how many 
acres. When the map is laid down by a scale of 
20 perches to an inch, then each rectangle will be 



TRIGONOMETRICAL SURVEYING. 



127 



16 perches by 10, or one acre; and if the map be 
40 perches to an inch, then each rectangle will be 
32 perches by 20, or 4 acres ; and if by 80 per- 
ches to an inch, then each rectan- 
gle will contain 16 acres. This 
instrument would be useful to 
gentlemen and others not very 
well skilled in surveying, to 
measure a map, or part of a 
map that they wished to know 
the content of nearly. It is 
easily used. The sides of the 
glass must be made to coincide with as many of 
the lines on the map as possible, and the broken 
squares can be estimated by the eye, or a square 
inch horn. 



Fig. 60. 



Description and design of a new instrument by which dis- 
tances can be found at once, without any calculation : 

Let a brass semi-circle (fig. 61) of about 9 inches 
radius, have its inner edge or limb, divided into 
90 equal parts, beginning at N and counting up- 
wards 10, 20, 30, &c., to 90 at Z, and each of 
these divisions subdivided into 6 equal parts. Let 



128 THE surveyor's GUIDE. 

the outer limb be divided into degrees and 6th 
parts of a degree, marking the degrees from the 
mi Idle of the limb, both ways, 10, 20, 30, &c., 
to 90 at N and Z. Let also, the middle space be- 
tween the outer and inner limbs, be marked from 
Z to N, 10, 20, 30; 40, &c., to 180 at N. 

Let this semi-circle be fixed to the middle of a 
box ruler B D, about S^ feet long, an inch and a 
half broad, and of a convenient thickness. The 
inner breadth of half this rule must be level with 
the surface of the semi-circle, but the outer half 
must be higher about two-tenths of an inch. On 
the outer half there must be fixed a thin brass 
scale of an equal length and breadth with the box 
ruler, the breadth of which scale is to be divided, 
by lines drawn from end to end, into three equal 
parts, and the length into inches, half inches, and 
tenth of an inch ; the inches are to be drawn di- 
rectly across the whole breadth, and marked 1, 2, 
8, 4, &c., both ways to B and D ; the half inches 
are to be drawn across the middle and innermost 
third, and the lOths only across the inner third. 
Let th/jre be on one end of this scale an inch, and 
in the other end half an inch, each divided very 



TRIGONOMETRICAL SURVEYING. 129 

exactly into 10 equal parts diagonally, that the 
lOths and centesms which may happen in the 
operations, on the square and indices hereafter to 
be described, may be exactly measured on them by 
a pair of dividers. The reason for raising the 
outer half of the box ruler above the inner half 
two-tenths of an inch, is to make room for the in- 
dices A b and A d, which are to be fixed to the 
centre of the semi-circle, and there to open and 
shut as occasion requires, like the legs of a sector. 
Those indices are about 26 inches long, three- 
fourths of an inch broad, and about two-tenths 
thick ; their breadth is to be divided into three 
equal parts, and their length into inches, half 
inches, and tenths, as the brass scale before men- 
tioned. The inches are to be marked from the 
center A, with 1, 2, 3, 4, &c., to b and d, and the 
tenths drawn across the inner third. Each of 
those indices must have a small screw nut with a 
pin or bit of wire upon it, which pin may, by the 
screw nut, be fixed exactly to any division on them 
in order to suspend the label, or ruler T Y, which 
has a thin piece of brass with a small hole in it, 
exactly fitting the aforesaid pin, and is to be fixed 
9 



130 THE surveyor's GUIDE. 

also to any division of the ruler, as occasion re- 
quires. Let this label, or ruler, be about two feet 
long, and of the same breadth and thickness as the 
indices A b and A d, and divided after the same 
manner as they are, only the tenths are to be 
drawn across the inner edge, as well as across the 
inner third of the breadth, and the inches are to 
be marked 1, 2, 3, 4, &c., from C to T and Y, 
making C T eighteen inches, and C Y six. The 
like divisions are to be made on the side of the 
square K X, beginning at the inner edge of the 
brass ruler at K, marking the full inches on the 
upper side, 1, 2, 3, 4, &c., to 24; the tenths are 
to be drawn across the upper third and the upper 
edge. Let this instrument be fixed on a tripod 
with a ball and socket like those of a common sur- 
veying instrument, but very strong, in order to 
have it very firm ; and let there be sights which 
may, as occasion requires, be fixed on the diame- 
ter, indices, and ruler T Y, of the the same kind 
with those of a surveying instrument. 

N. B, The ball and socket must not be fixed 
exactly under the center of the semi-circle, but some 
distance from it, on the cross-bar which goes from 



TRIGONOMETRICAL SURVEYING. 



131 



the center to the middle of the limb, as well to sup- 
port the head of the instrument more easily by be- 
ing nearer its center of gravity, as to make room 
for an air level, which must be fixed exactly under 
the diameter or ruler A B, so that when the semi- 
circle is turned vertically the diameter may be 
fixed horizontally. 




132 THE surveyor's guide. 

The use of the Instrument in measuring distances i" 
Example. 

Let it be required to find the distance from the 
house at A to the castle, (fig. 62) or to any part 
thereof, as the weather-cock on the top of the 
spire at C. 

Having set up your instrument at A, turn it 
about till through the sights on the diameter, you 
see a mark set up at B, and having fixed the di- 
ameter in that position, turn the moving index till 
through the narrow slit of a small sight fixed on 
the center, you see the hair in the other sight cut 
the spire at C, then fixing the index in that posi- 
tion to the limb of the semi-circle, measure with a 
four pole chain in a straight line from A to B ; 
and having marked the chains and links of that 
distance on the diameter and placed the ruler with 
the sights on it exactly to that distance, by means 
of the small pin and hole mentioned before, set up 
your instrument at the end of the distance you 
measured (which you may make full chains if you 
please) and turn it about till through the sights on 
the diameter you see a pole at the first station A, 
and having fixed it in that position, turn the ruler 
on the pin which is fixed at the former distance on 



TRIGONOMETRICAL SURVEYING. 133 

the diameter, till through the sights on it you see 
the vane at C ; then will the part of the index a c, 
cut by the inner edge of the ruler, give the dis- 
tance A C from the house to the spire at C, which 
was to be found ; and if there be occasion, the dis- 
tance from the mark at B to the spire will be found 
on the ruler at the intersection of the index ; all 
of which is plain from the similarity of the trian- 
gles ABC and a. pin. c, or that formed by the 
diameter, index, and ruler, from Cor. 1st 4 Euc. 
Book 6th. Thus the surveyor can find the distance 
of any or all the particular objects he can see and 
may wish to set down in his map, and by turning 
the instrument vertically by means of a notch in 
the socket, inaccessible heigths can, in like manner, 
be readily ascertained in the same manner. 

Example in Measuring Distance. 

Let it be required to find the distance from the 
house at A to the castle, (fig. 62) or to any part 
thereof, as the weather-cock at the top of the spire 
at C. 

Having set up your instrument at A, turn it 
about till through the sights on the diameter, you 
Bee a pole at B, and having fixed the diameter in 



134 



THE SURVEYOR S GUIDE. 



that position, turn the moving index till through 
the narrow slit of a small sight fixed on the center, 
you see the hair in the other sight cut the spire at 
C ; then fix the index in that position to the limb 
of the semi-circle and measure with your chain of 
100 links in a straight line from A to B, which 
mark on the diameter, and place the ruler, having 
the sights on it exactly on that distance by means 
of the small pin and hole before mentioned ; set 
up the instrument at the end of the measured dis- 
tance, and turn it about till through the sights on 




Fig. 62. 

the diameter you bisect the pole at A, and having 
fixed it in that position, turn the ruler on the pin 
which is fixed at the former distance on the diame- 
ter, till through the sights you see the vane at C ; 
then will the part of the index, a c, cut by the in- 



TRIGONOMETRICAL SURVEYING. 135 

ner edge of the ruler, give the distance A C from 
the house to the spire at C. 

And in like manner by directing the ruler to 
any other objects from A, and noting the degrees 
cut by the ruler on the limb, and directing from 
B to each object, the distance from A will be shown 
as before explained, and thus the surveyor fur- 
nished with such an instrument, can from the end 
of his first station, tell the length of his diagonals 
to as many corners as he can see from that point. 
Also, by turning the instrument vertically, heights 
can be determined in the same manner. 

I would recommend the surveyor to use a com- 
pass, having the limb divided into 360°, and the 
bottom of the box into four 90's ; then in taking 
the courses, if N. W., the limb and quarter com- 
pass are the same ; but if in the S. W. quarter, 
the sum of the degrees on the limb and quarter 
compass are 180° ; and in S. E. quarter, the dif- 
ference of the degrees on the limb and quarter 
compass make 180° ; lastly, if in the N. E. quar- 
ter, the sum of the quarter compass and limb 
make 360. A surveyor should prove all his courses 
by this rule before he quits his instrument. 



136 THE surveyor's guide. 

Problem. 
Given the bearings of any two stations of a 
survey, thence to determine the angle made by 
those stations. Rule — Deduct the preceding bear- 
ing from the succeeding, according as the remain- 
der is greater or less than 180°. Add — or+180° 
(as the case may be) and you have the required 
angle. 

N. B. The angle found by the above rule will 
be internal if the polygon lie towards the right 
hand in the traverse ; and external, if toward the 
left. 

Example First. 

Required the several angles of the polygon 
A B C D E F G, the courses of the sides being, viz . 




Fig. 





f" 






E 


1 


A B 26'9|° 


or 


S. E. 


891° 


2 


B C 2511 


or 


S. E. 


ni 


3 


C D 252| 


or 


S. E. 


72| 


4 


D E 1621 


or 


S. W. 


171 


5 


E F 77|- 


or 


N. W. 


77| 


6 


FG 30| 


or 


N. W. 


30f 


7 


GA 5f 


or 


N. W. 


5| 



TRIGONOMETRICAL SURVEYING. 137 

From 251^ From 77| 

take 269| take 162 J 

—18 — 84J 

+180 +180 

Sum 162= Ang. ABO. Sum 951= Z. D E F 

From 252| From 30| 

take 2511 take 77| 

+li —47 

+180 +180 

Sum 1811=/. BCD. Sum 133=/. E F G 

From 162^ From 5| 

take 252| take 30| 

—901 _25 

+180 +180 

Sum 891=/. CDE. Sum 155=/. F G A 

From 269J 
take 5| 

Bem. 263J 
—180 

Sum 831=/. GAB 
Now 180" multiplied by the number of sides in 



138 THE surveyor's guide. 

any polygon minus 360°, equals the sum of the in- 
ternal angles .-. 180X7= 160 and 1260—360=900 
So 83|+162+181^+89i+95|+133+155=900°. 
Proof. 

Next. Having the bearing of any station and 
all the* internal angles of any polygon, thence to 
determine the courses of each of the other stations 
in the regular order of succession, viz ; the land 
lying to the right hand as you surround it. Rule : 
According as the given angle is+or — than 180° ; 
add the preceding bearing, succeeding angle, and 
+or — 180° (as the case may be ;) their sum will be 
the succeeding bearing or course. 

Note. — It sometimes happens that the result 
will be more than 360° ; in this case take 360° 
from it and the remainder will be the course of ihe 

succeeding station. 

Example. 

Take the course of A B 269| or S. 89| E, in the 
preceding figure, and the angles as there found, 



TRIGONOMETRICAL SURVEYING. I'jQ 

269J 1621- 

1G2 95i 

+180 +180 

611^ 4371 

Deduct 360 360 

Cou. of B C 25 1| or S 711 E. Cou. of E F 77| or N 77| ^^ 

251J 77f 

18U 133 

—180 +180 

Cou. of C D 252f or S 72f E. 390| 

252f ^ 

_^-^gQ^ Cou. of F G 30f or N BOf W 

30f 

5221 155 

Deduct 360 +180 

Cou. of D E 162i or S 17f W. 365f 

360 

Cou. of G A 5| or N. 5f W. 

51 
83| 
+180 

Cou. of A B 269Jor S89|E. 

being the same as that given ; therefore, a proof 
of the correctness of the work. And thus the sur- 
veyor has a sure method of avoiding the inconve- 
nience of the needle being drawn from its true 
position by mines or other causes, and also correct 
the diurnal variation ; for no matter how much 



140 THE surveyor's GUIDE. 

the needle may be attracted at any station, the 
angle will be correct by taking a back and fore 
sight at every station, and having the true course 
of the first station. All the others can be found 
by the foregoing rules. And to know if any at- 
traction exists at the first station, take a course in 
a different direction from your chain line ; go to 
the object bisected, or to some convenient distance 
in that direction, and take a back sight ; if that 
agree with the fore sight, you may safely conclude 
that no attraction exists at either ; but should it 
differ, make trial in some other direction, in like 
manner, till you find what station the attraction ia 
in ; but by using a good theodolite all such trouble 
is avoided. 

In every survey that is truly taken, the sum of 
the Northings is equal to the sum of the Southings, 
and the sum of the Eastings to the sum of the 
VVestings. 

Let a b c e f g h represent a plot or parcel of 
land; let a be the first station, b the second, c the 
third, and so on. Let N S be a meridian line, then 
will all lines parallel thereto, which pass through the 



TRIGONOMETRICAL SURVEYING. 



141 




several stations, be a 
meridians also, as a o, 
b s, c d, &c., and the \ 
lines b 0, c s, d e, i 
&c., perpendiculars 
to these, will be east 
or west lines or de- 
parture. The northings e i+g o+h g=a o+b s-f 
c d+f r, the southings ; for let the figure be com' 
pleted, then it is plain that g o-fh g+r k=a o-f 
b s+c d and e i — r k=f r ; if to the former part 
of this first equation e i — r k, be added, and f r 
to the latter, then g o+h g+e i=a o+b s+c d+f r ; 
that is, the sum of the northing is equal to the sum 
of the southings. 

The eastings c s+q a=o b+d e+i f+r g+o h, 
the westings for a q+y o (a z)=d e+i f+r g+o h, 
and h o=c s — y o. If to the former part of this 
first equation c s — y o, be added, and b o to the 
latter, then c s+a q— o h+d e+i f+r g+o h ; that 
is, the sum of the eastings is equal to the sum of 
the westings. 

Now, as there is many methods of calculation, 
and every man chooses one in preference to all 



142 



THE surveyor's GUIDE. 



others, I shall here show the method which I have 
always practiced, being, I think, least liable to 
mistakes, although not the shortest, as shall bo 
hereafter shown. 



^ 


i i 




:::::: 

'i'.oo 

2.00 
2.00 
2.00 
1.00 


o 
o 




§§§§ !§§§§ : : i : i 


§ 


CO.-tOO.-l :r-l(>irH.-, ; ; ; ; ; 


3 


i 

If 

32 


o : 


: : '^ 

': : ? 


: : :o o o o o 












CO O CO CO : c<- 


iiS n 1 i i 




§ 


o c 


oggoogoooooo 

.-; c«5 o ,« rH- .-; o ^: o =o t^ o^ 






liislPSHis 










ooooo :ooo :o : 


o 


sii ^ ^ ^ 


liwum 


c^'cocscoc<;co--HC<ir-5(>;r4c^c^irqc<^l 




:2 






1 


p^ pq H w ^ W pq p4 a ^' ^' ^' ^' ^ 

'50^'^^^ur5coo'iooco''Oco^ 

;^' :^ «3 oQ M M M iz; aj M ai ;zh' oQ ^ 




^'1 


-^(MCO'^OOIt-OOOJOi-KNMtXiO 



o o 
•=> o 
o o 
o o 






a g 

S 

ttiO! 



In the above method the northings and south 
ings, eastings and westings, being corrected by the 



TRIGONOMETRICAL SURVEYING. 143 

foregoing rules, set the sum of the northings, or 
southings at the top of the column titled latitude, 
then continually add the northings and subtract 
the southings, or add the southings and subtract 
the northings, and the last number -will always be 
the same as the first, which is a proof of so much 
of the work. Then add the first and last latitudes 
together, and place their sum opposite to the first 
station in the column under latitudes, added, and so 
continue to add every two adjoining latitudes, and 
place their sum in a line with the latter, then mul- 
tiply each of these numbers by the particular 
easting or westing belonging to that station, and 
place the product in the column of east or west 
area, as the case may be, and the difference of 
these two columns divided by two, will be the con- 
tent of the survey. In this method there is no 
danger of making mistakes from indirect stations, 
and by using the eastings, and westings, in the same 
manner as you did the northings, and the south- 
ings, you can prove the work, and find the area 
four different ways. 



144 



THE SURVEYOR S GUIDE. 



ANOTHER METHOD, WHEREIN FEWER FIGURES ARE 
USED, NEVER BEFORE PUBLISHED: 

The Eastings and Westings, Northings and South- 
ings, are here corrected according to the foregoing 
rules, and placed as usual, as follows : 

CALCULATION OF THE NOTES ON THE SUCCEEDING 
PAGE. 



I I Lats. iDoub. Semi 

L. N.I L.S. 'added.! Rectangle. 



I B. I 



2.60 
0..36 
3.35 
3.34 
2.11 



1.75 

1.77 



2.76 
4.44 
0.77 
4.38 



0.40 
2.53 



15.28 15.28 
Double the sum of the indirect, 



6.04 
2.70 
0.59 
0.99 
3.52 
1.77 
0.00 



2.76 
9.96 
9.53 
4.38 
2.60 
6.56 
9.27 
8.74 
3.29 
1.58 
4.51 
5.29 
1.77 



+4.4712 

-1-11.9620 

-f-20.5848 

— 1.9272 

14.3520 

—10.3416 

-f-59.1426 

-j- 17.4800 

—4.4086 

-{-5.6564 

-h5.4120 

+5.0784 

+4.4958 



1.62 
1.20 



1.86 
Ex.W 
2.00 



3.58 
1.20 
0.96 
2.54 



165.3026 15.40 15.40 
33.3548 



Ex.K 
2.16 



5.621 



.9739 Angular spacoB. 



TRIGONOMETRICAL SURVEYINa. 



145 



11.76 Parallel breadth. 
12.35 Meridianal breadth. 

5880 
3528 
2352 
1176 

145.2360 Content of parallelogram. 
65.9739 



7,9.2621 
4 

3.70484 
40 



28.19360 

A.R. P. 

'7.3.28.19, the same as on next page. 



1 l\ 

i j \ 

i y 
1 / 

1 j 

i 

1 


if 




/l3 

i 
j 
i 


..... 




\ i 


1 ^ 



10 



Fig. 65. 



146 



THE surveyor's GUIDE. 



The foregoing plot and calculation may not be 
unacceptable to the reader, being as complicated a 
figure as could be easily met with. 

A new and concise method of Calculation, wherein fewer 
figures are used than in the common methods: 



2.60 
0.36 
3..35 
3.34 
2.11 



1.75 
1.77 



2.76 
4.44 
0.77 
4.38 



0.40 
2.53 



1.62 
1.20 

6.44 

L86 

'2.06 



3.58 
1.20 
0.96 
2.54 



3. 
4 

2, 
2, 

5.52 

7 
5. 

1.34! 6 



M. J). 
162 



24 E. 
44 E. 
28 E. 
72 E. 
80 W. 
94 W. 
32 W. 
32 W. 
66 W. 
08 W. 
88 W. 
92 W. 
2 E. 



86 E. 
68 E. 
72 E, 
00 E. 
08 W. 
74 W. 
26 W. 
64 W. 
98 W. 
74 W. 
96 AV. 
80 W. 
70 E. 



Area. 


Deduction. 


13.4136 




34.0992 




5.1744 




21.9000 




2080 




1.3464 




27.6710 




42 2176 




25 2778 






3.8960 




12.5488 


4.9000 





15.28 15.28 15.40 15.40 



A. R. 

7 3 



176.2080 17. 
17.6838 



2,0)15,8.5242 

7,9.2621 
4 



3,7.0484 
40 



28.19360 

This method may be called a compound of 
Burgh's and Gibson's, without being intimately 
connected with either. It allows the first meridian 
to pass at any distance from the first station not 
less than the first latitude or first departure. 



TRIGONOMETRICAL SURVEYING. 147 

This example supposes the first meridian to pass 
at the distance of the first Easting from the first 
station of the survey, and the M. D. column is 
completed by one single addition of the Eastings, 
or one single subtraction of the Westings, to or 
from each preceding one, agreeably to the nature 
of the signs. The D. D., or double distance col- 
umn, is completed by adding the first and last, 
and placing their sum in a line with the first East- 
ing or Westing, and then adding every two ac- 
cording to the signs, and placing their sum in a 
line with the latter, marking E. or W. as the case 
may be. Then the Eastings X by the Southings, 
and the Westings X by the Northings, must be put 
into the area column ; but, the Westings X by the 
Southings, and the Eastings X by the Northings, 
must be put into the deduction column, the differ- 
ence is double the area of the survey. 

The following is a method of calculation first 
published by Noble, the inventor, and is a very 
superior plan when well understood, but requires 
considerable attention to distinguish the indirect 
stations, as the areas belonging to them must be 
deducted. A little practice will enable the learner 
to know both them and the four extremes, viz : 



148 THE surveyor's guide. 

N. S. E. and W. That author's description of a 
semi-rectangle is a figure limited by the latitudes 
of both ends of the station, the station itself, and 
a section of the parallel from which the latitudes 
are measured, equal to the departure ; and when 
the last mentioned is indirect, the semi-rectangle 
is indirect also, viz : Indirect or retrograde sta- 
tions are those stations, in respect of the rest, 
which bear backward or contrary to the natural 
succession of the four quarters of the compass. 

If, in proceeding Southerly from the extreme 
point North, there happen a station to turn North- 
erly, or, in proceeding Northerly from the extreme 
point South, there happen a station to turn South- 
erly, such stations are indirect or retrograde sta- 
tions. The same may be said of stations that 
turn after the like manner in proceeding from the 
extreme points E. and W. of the survey. The 
extreme points, N. S. E. or W. of a survey, are 
the ends of those stations which run more to the 
N. S. E. or W. than any other stations in the survey. 

Though most surveys have those four extreme 
points, yet there are some where one and the same 
station may be the greatest extreme N., and at 
the same time the greatest extreme East or West ; 



TRIGONOMETRICAL SURVEYING. 149 

or one and the same station may be the extreme 
South, and likewise the extreme East or West. 
The circumscribing parallelogram of a survey is a 
rectangle or parallelogram circumscribing the body 
of the land, whose four sides, passing through the 
four extremes N. S. E. and W. of the survey, are 
two meridians and two parallels of latitude. 

The angular spaces are the areas contained 
between the sides of the circumscribing paralello- 
gram, and the stations of the land surrounded, 
which, deducted from the area of the second parall- 
elogram, leaves the content of the survey. 

Now in order to find the area of those angular 
spaces, the four extremes must first be ascertained. 
This an experienced hand can see at once by 
examining his field-book, which, being known, you 
must find the latitude of each station in the survej' 
from the extreme points North and South ; thus, 
having found and corrected your latitudes and 
departures, and placed them as in the following 
table, write in a line with N, and also the South 
extreme as in the following table. Now, begin- 
ning at each of these extremes, North and South, 
continue to add the Northings, and subtract the 
Southings to find the latitude of each station to 



150 THE surveyor's GUIDE. 

the extreme point West, but you must still add 
the Southings and subtract the Northings to the 
extreme point East. When the latitude of every 
station is thus found, and placed in their proper 
columns, add every two latitudes next each other, 
and put their sum in a line with the latter station 
in the column marked L. A., and each sum or 
number in this column is the length of a rectangle, 
which is double the semi-rectangle of each station. 
It is no matter at which of the two latitudes you 
begin, so that you place their sum in a line with 
the latter or succeeding station ; but it is common 
to begin by adding the first and last stations to- 
gether, and placing their sum in a line with the 
first station ; then add the first and second, and 
place it in a line with the second, and so on 
till the column is filled. Then each number must 
be multiplied by its corresponding Easting or 
Westing, and the products put in the column 
marked D. S., or double semi-rectangle of each 
station. If the Easting or Westing be direct 
then this product must be marked f ; but if it be 
indirect, with the negative sign — , and the sum 
of all the affirmatives, abating the sum of all the 
negatives, will be the content of all the angular 



TRiaONOMETRICAL SURVEYING. 



151 



spaces. But, to find the length and breadth of 
the circumscribing parallelogram, note that from 
the sum of all the Northings or Southings you 
must deduct the sum of all the Northings or South- 
ings that have indirect difference of latitude, 
which will give one side, and the same must be 
done with the Eastings and Westings to find the 
other side. The length and breadth of the parall- 
elogram being thus found, they must be multiplied 
together, and from their product take the content 
of the angular spaces, and the remainder will be 
the content of the survey. 

TAKE THE FOLLOWING EXAMPLE IN NUMBERS. 



9.23 
9.04 
4.66 
1 51 



6.78 
17.46 
12.97 
11.76 



6.17 
1.61 
0.00 
6.78 
24.24 
37.21 



6.00 
30.28 
39.51 
48.55 



5.75 

30.28 

69.79 

88.06 

7.68 

1.51 

6.78 

31.02 

61.45 

86.18 





E. 


W. 


+076.5900 




13.32 


+468.7344 





15.48 


+687.4315 




9.85 


+626.1066 




7.11 


+088.9344 


n.58 




+020.2340 


13.40 





+049.8330 


7.35 




+268.3230 


8.65 




— 233.5100 




3.80 


+739.4244 


8.58 





54.72 54.72 



2)2792.1013 49.56 49.; 



1396.0506=Ang. spaces. 

In this example there are no indirect stations 
in the Northings or Southings, 54.72 is the me- 
ridianal breadth of the survey. But station 9th 
being indirect in the parallel breadth, must be 



152 THE surveyor's guide. 

deducted from the sum of the Easting or Westing 
to find the other side of the circumscribing par- 
allelogram. Thus : 

49.56 Sum E. or W. 
3.80 Indirect. 



45.76=Parallel breadth. 
54.72=Meridianal breadth. 



91.52 
32032 
18304 
22880 

2503.9872 Content of circum. parallelogram. 
1396.0506 " of the angular spaces. 

1107.9366 
4 



3.17464 
40 



6.98560 lib. 3.06.98, the content. 

In this example you may see that the four ex- 
tremes are the 6th, 1st, 10th, and 4th stations 
You can also see that the two latitudes of the 
extreme West is equal to the two latitudes of the 
extreme East, that is 6.17+48.55=48.97+5.75, 
which is a proof to so much of the work. 



TRIGONOMETRICAL SURVEYING. 



153 



If you begin with the Eastings and Westings, 
and proceed as you were directed, all along with 
the Northings and Southings, you can find the 
content of the survey in like manner, and so prove 
the work. 

To survey with the compass through any mine, or other 
cause for drawing the compass needle off its parallelism : 

The diurnal variation of the needle is known 
to every practical surveyor, but is easily cor- 
rected by examining the time of the day when the 
courses of long stations were taken ; as from about 
8 o'clock in the morning till about 2 in the after- 
noon, the needle varies Westerly to from about 
7'08" to about 13'21", as shown in the following 
table. The surveyor can make such allowance as 
will (all other errors apart) insure a complete 
clase. 

MEAN DIURNAL VARIATION FOR EVERY MONTH IN 
THE YEAR. 



January, 


0" 7'08" 


July, 


0'a3'14" 


February, 


8'58" 


August, 


12'19" 


March, 


IVll" 


September, 


11'43" 


April, 


12'26" 


October, 


10'36" 


May, 


13'00" 


November, 


8'09" 


June, 


13'21" 


December, 


6'58" 



154 ' THE surveyor's guide. 

Now, in surveying with the compass detached 
from a Theodolite, both back and fore sights 
should always be taken ; and to make sure that no 
attraction exists in the first station, take a course 
in a contrary direction to some object, go to that 
object and take a back sight ; if the fore and back 
sight agree you may be satisfied that no attraction 
is at your first station ; but should they not agree, 
you must then, from the latter station, repeat the 
like process till you find at which of them the 
attraction exists; if, at 'the first station, either 
note its quantity, which allow on the next course, 
as in tracing old boundaries ; or pay no attention 
to it at the starting, but continue to take the fore 
and back sights throughout, and as at any station 
the needle will be as much attracted at the fore as 
the back sight, the angles can all be truly found as 
formerly shown, and thence the true courses for 
calculation by latitude and departure. Thus may 
the expert surveyor traverse any city, mountain, or 
other place containing mines or other substances 
which attract the needle, about which I have heard 
many complaints. 



TRIGONOMETRICAL SURVEYING. 



155 



Now to plot the last given notes, and in like 
manner any other survey similarly prepared : — 
Having the length and breadth of the circumscri- 
bing parallelogram, let it be drawn by the same 




nc-le you intend to lay down your map by, and 
beginning at either of the extremes, as 1, lay off 
your latitude as l.a 5.575, and at right angles to 
that, the departure of that station or Westing a.2 
13.32, and join their extremities with the line 1 2, 



156 THE surveyor's guide. 

which is the distance. The next' station is Ic-:, W, 
Draw toward the North 2.b parallel to the sides 
of your parallelogram, and on it lay 30.28, your 
next Northing, and at right angles thereto toward 
the West 15.48, your next Westing, and join 2 and 
3, which is your next distance, and so on all round, 
and as your Northings are equal to your Southings, 
and your Eastings to your Westings, your last 
departure, whether East or West, will fall into the 
point of beginning, as T.l. This is the most expe- 
ditious mode of plotting surveys, and can be made 
use of in the most extensive work, and is much 
superior to protraction by parallels and a metallic 
protractor. The mechanical methods of finding 
area, shown by many authors, I do not think well 
to notice, as none of them can be depended on for 
accuracy. 

OF LOTTING OR LAYING OUT TOWNS, &C. 

llegarding this kind of surveying, little can be 
said more than giving some general directions con- 
cerning the method of operation, as every man has 
mostly predetermined the manner in which he 
Intends to have his property cut up into lots. 
Provide yourself with a 20 or 25 feet pole, ten 



TRIGONOMETRICAL SURVEYING. 157 

skivers with sharp points and thin edges, two brass 
plummets with steel points hung to fine cords ; 
then having fixed poles so as to direct you in a 
straight line, and set them perpendicular by the 
help of your plumb, direct your assistant to hold 
one end of your pole in the straight course, with 
his plummet hanging over the extremity, whilst 
you hold yours touching the end of the pole which 
you hold, and the point of your plummet exactly 
over the starting point ; when both plummets are 
steady, order your assistant to stick, and exactly 
where the point sticks, he sticks one of his skivers 
edgewise and slanting, so as that you can, when 
you arrive at it, hang the point of your plummet 
exactly over the edge of the skiver, and your 
assistant again sticks his plummet in the ground, 
and a skiver as before, and so on to the end. By 
measuring carefully in this manner, property can 
be laid out with great accuracy. 

Almost every man has his own method of keep- 
ing his field-book, but the following method, which 
I have always adopted, is, I think, best calculated 
to prevent confusion in extensive surveys, for as 
writing backward and chaining forward are con- 
trary, it is more congenial, and natural, to both 



158 THE surveyor's guide. 

write and chain forward, by beginning at the bot- 
tom of the page. 

N. B. It may not be unacceptable to the reader 
CO see these notes, calculated by Noble's meinod, 
as on page 119. 



TRIGONOMETRICAL SURVEYING. 



169 



Maple 


60.00 
35.10 

N.77fW. 


Pin Oak 
0.5 






i 
1 


W. 0. 


(5) 








i 




Stump. 


„^ 










1 


41.40 












162} 










"a 


S. 17f W. 










1 

1^ 


(4) 


To a stone. 


1 




To the place ef 


36.40 


18.48 


"" 0.6 


33.00 






beginning. 




@ 




1 


m 






21.00 




7.10 


R. 0. 




m 


S. 0. 




3.24 


0.15 to a Pine 








N. 5f E. 


s 




15.00 


0.10 




(7) 




7.00 
2521 

S. 72|E. 


toChesnut 










m 




J^ 




1 B.Oak 


(3) 


To a post. 


t 


36.25 

m 

23.00 


To a post. 
Chesnut. 


41.00 


m 


26.00 
4.00 


Dogwood 






"2 


25 If 


m 


S 


10.00 


0.10 to a Beech 


2 

w 
o 


S. 71fE. 

(2) 




7.00 

N.30-IW. 

(6) 


m 






20.00 
269J 


chains to a 
hickory 




9 


Shellbark 
Hickory. 




S. 89*E. 
(1) 


tree. 




66.00 


Stream North 








62.00 


36 West. 



Begins at a White Oak on Squire Hays' Estate. 



160 



THE SURVEYOR S GUIDE. 



The foregoing method of keeping a fiehi book, 
I think, is the most convenient I have seen. The 
following is the calculation of the notes corrected 
by the foregoing rules. 



7^E. 
.Ti%W. 



F. 
Poles, 



10.00 
20.50 
18.40 
20.90 
33.00 
18.25 
9.48 



5.50 
19.90 



31.95 
25.40 
19.90 
0.00 



64.00 
57.35 
45.30 
19.90 
6.94 
29.56 
64.67 



640.0000 
1115.4575 
795.9210 



126.9620 
223.8150 
275.7948 



2602.7683 626.5718 47.96 47.96 
626.5718 



2.0)1976.: 



in square four polo 
chains. 



A. R. P. 

M.3.0967 







Lat. 


Lat. 


Lats. 


Double Semi- 






N. 


S. 


South. 


North. 


Added. 


rectangles. 


E. 


W. 




0.10 




0.10 


0.10 


—1.0000 


10.00 






6.55 




6.65 


6.75 


+131.2875 


19.45 






5.50 


19.90 


12.15 


18.80 


+330.3160 


17.57 


Ex.E. 


Ex. S. 


19.90 


00.00 




19.90 


—128.9620 




6.38 


6.94 




6.94 




6.94 


+223.8150 




32.25 


15 68 




22.62 


9.43 


29.56 


+275.7&48 


Ex. W. 


9.33 


9.43 


North. 




00.00 


9.43 


+8.8&42 


0.94 





32.05 32.05 
Content of the angular spaces, 



TRIGONOMETRICAL SURVEYING. 161 



47.96 Parallel breadth. 
32.05 


23980 
9592 

14388 




1537.1180 Content of circum. parallelogram. 
549.0197 " of the angular spaces. 


988.0983 
4 




3.23932 
40 


A. R. P. 

98.3.95.73 the same as before. 



9,57280 ^ 

There are no indirect stations in the above, but 
were the longitudes made use of instead of the 
latitudes, the last station would be indirect; and 
here also it may be seen that the sum of the oppo- 
site latitudes, against the extremes East and West, 
are equal, viz : 12.16+19.90=32.05 and 22.62+ 
9.43=32.05. 

Of the Tracing of Old Hearings. 

Gummer, in his work on Surveying, gives the 

general number 57.3°, for doing this which many 
11 



162 THE surveyor's guide. 

work with, although it is not correct, but comes 
out pretty near the truth when the chain line is not 
very long. 

To find this number, say 6.2831853 (the circum- 
ference of a circle whose diameter is 2) : 360° :: 1 
: 57.3° nearly. Now if two corners are known, 
and can be both seen, set your compass at one of 
them, and direct your sights to the other ; the dif- 
ference between that shown by your needle, and 
that shown in the deed, will be the variation to be 
allowed on each course round the land, supposing 
all those given in the deed to have been correctly 
taken at the time the survey was made, which fre- 
quently happens not to be the case. If the two 
corners cannot be seen from each other, run the 
course and distance given in the deed, and observe 
if the point you arrive at, joined to the corner, 
form an isosceles triangle, which will be the case 
if all be right ; otherwise some mistake has been 
made in the distances, which must be corrected. 
Then take the pendicular distance to the given 
corner, and say : As the measured distance is to 
the distance to the corner, so are 57.3° to the 
number of degrees, minutes, or seconds, as the 
case may be, wtiich will be the variation. Or, 



TRIGONOMETRICAL SURVEYING. 163 

more accm-ately. As the distance to where the 
perpendicular was taken is to radius, so is the dis- 
tance to the corner to the tangent of the variation. 
In running your trial line, you will be told you are 
wrong, and that you don't understand your busi- 
ness, and all such stuff, will be sounded in your 
ears ; but pay no attention to such nonsense, for it 
is to be regretted that too many men are so igno- 
rant as to think that a Surveyor can, by some 
mysterious means, direct his compass on the exact 
line, and find all the courses as if by magic. It 
often happens that the corners runs through clumps 
of trees or other obstructions through which you 
cannot chain. In such a case I have often chosen 
an opening some degrees to right or left of the 
fence, and at certain distances driven posts till I 
found a perpendicular to the corner. Then, as 
the whole distance is to the perpendicular, so is 
each distance from the beginning to the perpen- 
dicular distance from the measured line to the 
fence, which, being correctly laid off, and posts 
driven at their extremities, will point out the true 

boundary. 

Of Levelling. 

The art of levelling consists in finding or tra- 



164 THE surveyor's guide. 

cing a line on a given portion of the earth's sur- 
face, parallel to the horizon at all points. The 
subject is too extensive to be comprised in this 
small treatise. I shall give an example, which it 
is hoped will enable the reader to do anything of 
that nature that may come in his way. Any one 
desirous of being fully informed on that subject, 
should consult BrufF's Engineering, where every 
information on that subject can be obtained. Re- 
garding the adjustment of the level, which is a 
simple matter, let the practitioner always place his 
level in the middle, between the back and fore- 
sights, and keep the bubble in the middle of the 
divisions, and all will be right. 



TRIGONOMETRICAL SURVEYING. 



165 



riELD BOOK DISTANCES, MEASURED WITH A 
HUNDRED FEET CHAIN. 



Eleva- 
tion. 


Back 
sight. 


Fore 

sight. 


"rr 


Total 
elevat'n 
Datum 

100 feet. 


Dis- 
tance. 


Eemarks. 


1.11 


6.84 
5.73 
8.10 
8.15 
5.80 
5.00 
5.01 
4.05 
4.98 
6.12 
2.25 
7.77 
3.95 
6.30 
1.60 
4.24 
6.74 
2.17 
4.60 
5.36 


5.73 
8.10 
8.15 
5.80 
5.00 
4.55 
4.05 
4.98 
6.12 
6.67 
7.77 

13.52 
6.30 

10.80 
4.24 
6.74 

10.20 
4.60 
5.36 
5.99 




100. 
101.11 

98.74 
98.69 
101.04 
101.84 
102.29 
103.26 
102.32 
101.18 
100.63 
96.11 
89.36 
87.01 
82.61 
79.87 
77.37 
7.3.91 
71.48 
70.72 
70.09 


.00 

100 

100 

100 

100 

100 

100 

100 

100 

100 

100 

100 

100 

100 

100 

100 

100 

100 

100 

100 

100 


"1 On cross road 50 
J ft. W. N. 54 W. 
) Side of ravine, 30 
J feet deep. 
10. bottom 10 ftwd. 
] Top of bank on 
J other side. 

> Middle of stream, 
i N. 57 W. 

im at top, from which 
luced level is deducted, 
a third proof of the 
cy of the work. 


2.37 
0.05 




2.35 
0.80 
0.45 
0.96 








0.93 
1.14 
.56 
5.62 
6.76 
2.36 
4.50 
2.64 
2.50 
3.46 
2.43 
0.76 
0.63 




























5.67 


104.76 


134.67 
104.76 

29.91 


35.58 
5.67 


100.... 
70.09 


1 Dat. 
! the ret 

[giving 


29.91 


29.91 


J accura 



The fall in the following section from 1 to 21 
is 29.91 feet; this divided into 2100 feet, the 
whole distance gives 1 in 70.21, the regular grade ; 
and to find the grade in degrees, it will be as 2100 
is to radius :: 29.91 to the tangent of the angle in 
this case 0° 49' nearly. Here it will be observed 



166 



THE SURVEYOR'S GUIDE. 



that the difference between the datum line and any 
grade, is the height above or below the base line, 
running through the first station. If the ordinate 
be greater, the difference is above base ; if less, 
below. Some old fashioned levellers follow a more 
intricate plan. Thus 101.11—98.74=2.37—1.11 
=1.26 above; again, 98.74—98.69=0.05, and 
1.26+0.05=131 below, and so on. But this re- 
quires too much thought, when to add and when 
to subtract ; whereas the other method is done by 
one subtraction. 




Fig. 67. 



inn woXlOD ipa wo ioo\ioo WO lOO lon lUO mo looiioo lOoXioo ioo\ioo loo\ioo 
Scale of length, 800 feet to an inch— of height, 100 



To LAY OUT A Road on a Regular Grade up 

A Hill. 

Set your instrument at the starting point, level 

it, and set the vane on your levelling rod to the 

exact height of the centre of your glass. Ele- 



TRIGONOMETRICAL SURVEYING. 



167 



Vate your grading instrument to the number of 
degrees you intend your road to be. Send forward 
your rod to any place where the cross wire will cut 
the middle of the vane, and there drive a post, and 
on it mark grade, and so on to the end of the 
road. And to find the cuttings and fillings, the 
following flan is the most convenient. Set your 
instrument on the starting point, measure very 
exactly the height of the centre of the glass, and 
send your rod to the first point where cutting or 
filling is required. Elevate your instrument to 
the grade, mark where it cuts the rod, and the dif- 
ference of the height of the instrument and height 
on the rod, will be the cutting or filling. If the 
height of the instrument exceeds that on the rod, 
the difference is cutting, and per contra. 

Example : 




Fig. 68. 

In the above cut the height of instrument is 4 
feet ; height of rod, 2 ; difference, 2 cutting. 



168 THE surveyor's guide. 

Again, height of instrument, 4, and back sight to 
rod 5 ; difference, 1 to be added to last, gives 3 
of cutting at instrument. Fore sight, 3 ; differ- 
ence to be added to last, gives 4 feet cutting at the 
rod ; but now, height of instrument, 5; back sight, 
2 ; difference, 3 ; which, deducted from 4, leavea 
1, and so through the whole. 

To Inflect in Curves on Rail Roads and 
OtherSo 

The curves most in use at the present time, are 
those of a circle. The angle made at the angular 
point of the tangents is always given — the length 
of your tangent is also given. To find the radius, 
multiply the natural tangent of half the contained 
angle by the length of the tangent of your curve, 
and the product will be the radius of the curve. 

To find the degree of curvature, divide half the 
chord to be inflected by the radius of the curve, 
and it gives the natural sine of the degrees of cur- 
vature. 

Thus, in the annexed figure, where the radius is 
140, and the cord to be inflected 100. 140)50, 
000000 (.357142 is the natural sine of 20° 55' = 
the decrees of curvature. 



TRIGONOMETRICAL SURVEYING. 



169 



Demonstration. 

The angle A D C, is a right L=to A D B, and 
^ C B is common to the two triangles, A B C and 
A D B. Hence LAG D=B A Di the L angle 
of deflection. Now set your instrument at A, 
direct your index to E, turn it towards the curve 




till 20° 55' are told on the limb, holding the end 
of your chain at A ; let the assistant hold the 
chain tight, and move round till the other end 
comes in the line of the perpendicular wire of tho 



170 THE SUEVEYOR'S GUIDE. 

telescope at G, and then fix a pin. Again, if 
nothing intervene to prevent your seeing, inflect 
from A E, double the said /., and fixing one end 
of the chain at G, let the other be stretched to 
come in contact with the telescope at H, and so on 
through the whole. If II cannot be seen from A, 
move the instrument to G, and take a back sight 
to A, and inflect double the L of the degrees of 
3urvature from G K, which will fall into H. 

I have met with some calling themselves engi- 
neers, who adopt the following plan. They divide 
57.,3°X60=3438' by the radius of the circle, mul- 
tiplying the quotient by the number of feet in the 
chord, and divide by 60 for double the angle ; but 
this is erroneous. I remember having met Avith a 
person who declared that the angle found by this 
rule was the true angle of deflection. I gave him 
the tangent 100, and the radius 100 feet, and he 
did it by this rule, viz: 100)3438(34.38X100= 
3438-1-60=57° 18'. In this instance the L made 
by the tangent and chord is only 45°, so that in- 
stead of inflecting in 100 feet, this 57° 18' would 
fall below the chord. Nor is the half of it cor- 
rect, viz: 28° 39'. For by the true method 
100)50(=,5, the natural sine of 30° the true angle. 



TRIGONOMETRICAL SURVEYING. 171 

It remains to find the length of the curve A G 
H F. The circumference of a circle whose di- 
ameter is 2, is 6.2832 nearly. Hence as 360° : 
6.?832 :: 1 : .01745, &c. This number, multi- 
plijd by the degrees in the arc, and by the radius 
oi the curve, gives the length of the arc, thus : 

01745 
11 



17450 268.£ the length of the arc, and 
1745 so of any other. 



1,91950 
140 

7678000 
191950 

268,73000 



The two following problems may be amusing to 
some readers, viz : 

A gentleman has a lot 40 perches long and 30 
perches wide. He thinks the ends may be so ap- 
plied, as that when their extremities are joined, the 
area may be the greatest possible. The perpcn- 



172 THE surveyor's guide. 

dicular breadth, and the length of the unknowr 
side are required. 

Answer: Breadth, 26.815 nearly. 
Length of the unknown side, 66.904 nearly. 

Problem Second. 

A plank road is to be made from the city A to 
the town B, 20 miles asunder. A straight road is 
so situated that a perpendicular from A to it is 10 
miles, and from B 6 miles. The plank road must 
touch the straight road in such a point as to be 
the shortest possible by that route, the length of 
the plank road, the point of contact, and radius 
of the curve havmg 200 feet tangent, are required. 

Answer: Length of the pJank road, 25.298 
The distance of the point of contact 

from A, 12.2474 

And from B, 7.3484 

Radius of the curve havii^g 200 feet tangent, 
245 feet nearly. 

This note to be placed after the calculation of 
the large triangle. It is there shown that the area 
of any plane triangle, the three sides of Tviiieh are 
given, IS A B^. Sine B. Sine A 



C 2 Sine C. Which it thus 

proved BAA 



TRIGONOMETRICAL SURVEYING. 173 

It has been already shown that B C. B A. Sine B. 

equal area of the triangle, .'. B C. A C. Sine C. 



2 
Hence B C. B A. Sine B=B C. A C. Sine C. 

Multiply each side by B A, and we have 

B C. B A^ Sine B=B C. A C. B A. Sine 0. 

Divide this equation by B C, we have 

B A'^. Sine B=A C, B A. Sine C. 

Multiply each side by Sine A .*. 

B A^ Sine B. Sine A=A C. B A. Sine A. Sine C. 

Divide this by Sine C, and 

B A^ Sine B. Sine A. 

=A C. B A. Sine A.=twice 

SineC 
the area, and therefore 

A B^ Sine B. Sine A 

=Area 

2 Sine C 
To find the perpendicular ordinates from the 
chord 6 of any arc of a railroad, in order to set off 
the curve correctly and speedily, without the help 
of an instrument, suppose it to be a 20° curve, the 
tangent 200. Find the radius, as formerly taught ; 
multiply the radius by the natural co. sine of half 
the vertical angle, and you have J the chord. 



174 



THE surveyor's GUIDE. 



Multiply the radius by the natural sine of the 
same angle, and you have the distance from the 
centre to the middle of the chord, a constant num- 
ber to be deducted. Now take any distance, sup- 
nose 10 feet, at which you choose to erect your 



^ 



/I 



'v '(In? 




Fig. 70. 



ordinates, and from the semi-chord subtract thia 
number, square the remainder, and subtract it 
from the square of the radius ; extract the square 
root, from which take the aforesaid constant num- 
ber, and the remainder is the ordinate to be 
rightly applied, and so proceed till you arrive at 



TRIGONOMETRICAL SURVEYING. 175 

the middle of the chord ; then the dijBFerence be- 
tween the said constant number and the radius, is 
the versed sine or greatest ordinate, and now you 
are prepared to lay off the other side of your 
curve, and all this can be done in a few minutes in 
the field. 

Example. See last figure. 

Nat. tangent of 80°=5.67128 
200 



1134,25600=Radius, 1134. 
Nat. CO. sine of 80° =,17365 



5671280 
6805536 
3402768 
7939792 
1134256 



196,96355440=Semi -chord, 197. 



Nat. sine of 80° 1134 

,9848 



9072 
4536 
9072 
10206 



lllfi 7fi5^9 Distance from centre to saM 
XL±V,^VO^ chord=m7. 



176 THE surveyor's guide. 

From 1134 
Take 1117 

17= Versed sine FE— From 197 
Take 10 

(187)==34969 

From (1134)^=1285956 
Take ( 187)^= 34969 

1250987=1118 
From which take 1117 

1 ft. the 1st ordinate. 

Again, for the 2d ordinate, 197— 20=(177)^ 

=31329 and 1285956 
_ 31329 

(1120 From 1120 

^/ 1254627 Take 1117 

1 

— 3=the next. 

21)25 
21 

222)446 
444 

2240)227 

Ordinate. All this is plain from the figure, and 
when the radius and constant subtrahend aie 



TRIGONOMETRICAL SURVE^'ING. 177 

found (which is only the work of a minute) all tlic 
others are nearly had at sight. This I consider 
quite superior to any other method now^ in practice 
Otherwise thus : Let the radius, versed sine, 
chord, and constant quantity D E, be found as 




before, divide the semi-chord into any numbei of 
parts as e f g h i. From E C deduct one of the 
pnrts i C, leaves E i=m F, then D F=(radius^, 
squared — (m F)^=(m D)^ the square root of which, 
minus the constant quantity, E D, gives the ordi- 
nate i F, and in like manner all the others are 
found, and thus the curve can be laid off in a few 
minutes in the most accurate manner, (by the 47th 
of the first of Euclid.) 
13 



178 



THE SURVEYOR S GUIDE. 



i'ROBLEM. 
Let A B C be a right angled triangle, the hy- 
pothenuse of which is 35, and the difference be- 
tween the area of the enscribed square (one of 
c whose angles coin- 
cides with the right 
angle of the trian- 
gle) and the area 
of the A is 150. 
Required the sides 
of the triangle. 



Fig. 72. 




Solution. 

Put A E=x and D F=y. Then per 4th Euc. 
bth, y : J :: X : f=CF,f+x j=Double the 
area of the As A D E and DEC .-.=300 or ^f -f 
2 X y=600. Also f + Y=B C and x+y = A 

B. Now (ZVy)'+(x + y)'=35^ viz: l^+'^' + y* 
+y+2 X y=1225 
Deduct '^' +2 X y=600 



Root and 



Z^_l_2 y''+x^=625 Ex't the square. 

-^'+x=25 or 



■x==25 X 



:A D==5 V X. 



TRIGONOxMETRICAL SURVEYINQ. 179 

Hence 5 V x : x :: 35 : x+y, and by divi- 
ding the first and third by 5. x| : x :: y x+i 
and :: are their squares, x : x^ :: 49 . x^ fy^-" 
2 X y. Multiply the extremes and means, and 

49 x2=x"+x y-+2 x^ y-^by x and 
From 49 x =x^+y=2 x y ; but 25 x=y-+x^ .*. 
Take 25 x =x^+y^ 

24 X ^ 2 X y or 
24 = 2 y and 

y =12 the side of the square. 
.And the sides of the angle are 21 and 28. 

28 
21 

28 
56 

2)588 

294=area of A. 
Deduct, 144 

150-.-area of the 2 A's. 



180 



THE surveyor's GUIDE. 



;' 


TABLES OF LATITUDE AND DEPARTURE. ]' 




N. S. 


E. W. |N. S. |E. W. 1 


N. S. 


E.W. 


N. S. E.W. 


1 







Oi 


191 1 


Oi 
0.9999 


89i 


Oi 89i 
0.9999]0.0131 




0.9999 


0.0043 


0.0087 


f, 






1.9999 


0.0087' 


1.9999 


0.0174 


1.9998 0.0262 


3 






2.9999 0.01311 


2.9998 


0.0261 


2.9997 


0.0392 


4 






3.9999 0.0174! 


3.9998 


0.0349 


3.9996 


0.0623 


5 






4.9999 


0.0218 


4.9998 


0.0436 


4.9995 


0.06.64 


fi 






5.9999 


0.0262 


5.9997 


0.0623J 


5.9994 


0.0785 


7 






6.9999 


0.0305 


6.9997 


O.O6I1I 


6.9993J0.0916 1 


fi 






7.9999 


0.0349 


7.9997 


0.0698' 


7.9992 0.1047 | 


9 




89° 


8.9999 


0.0393 


8.9996 0.0785, 


8.9991 
li 


0.1178 


1° 


li 


I'i 


88i 1 


1 


0.9998 


0.0174 


0.9997 


0.0218 


0.9996 


0.0262 


0.9995 


0.0305 


f, 


1.9997 


0.0349 


jl.9995 


0.0436 


1.9993 


0.0523 


1.9990 


0.0610 


8 


2.9995 


0.0523 


12.9993 


0.0654 


2.9989 


0.0785 


2.9986 


0.0916 


\ 


■^ 9994 


0.0698 


13.9990 


0.0872 


3.9986 


0.1047 


3.9981 


0.1221 


ti 


4.9992 


0.0872 


14.9988 


0.1090 


4.9982 


0.1309 


4.9976 


0.1527 


fi 


5.9991 


0.1047 


15.9986 


0.1309 


6.9979 


0.1570 


6.9972 


0.1832 


7 


6.9989 


0.1221 


16.9983 


0.1527 


6.9976 


0.18321 


6.9967 


0.2137 


8 


7.9988 


0.1396 17.9981 


0.1745 


7.9972 


0.2094 


7.9962 


0.2443 


9 
1 


8.9886 
2° 


0.1570 


8.9978 
0.9992 


0.1963 
0.0392 


8.9969 


0.2356 


8.9968 


0.2748 
87i 


88° 
0.0349 


2i 


87i 


0.9994 


0.9990 


0.0436 


0.9988,0.0479 i 


9 


1.9987 


0.0698 


1.9984 


0.0785 


1.9981 


0.0872 


1.997710.0969 | 


S 


2.9981 


0.1047 


2.9977 


0.1178 


2.9971 


0.1308 


2.9965 


0.1439 


4 


3.9975 


0.1396 


3.9969 


0.1570 


3.9962 


0.1745 


3.9964 


0.1919 




4.9969 


0.1745 


'4.9961 


0.1963 


4.9962 


0.2181 


4.9942 


0.2399 


6 


5.9963 


0.2094 


5.9954 


0.2365 


15.9943 


0.2617 


5.9931 


0.2878 


7 


6.9957 


0.2443 


6.9946 


0.2748 


6.9933 


0.3053 


6.9919 


0.3358 


8 


7.9951 


0.2792 


7.9938 


0.3141 


7.9924 


0.3489 


7.9908 0.3838 1 


9^8.9945 


0.3141 

87° 

0.0523 


8.9930 

3i° 

0.9984 


0.3533 

861 
0.0567 


8.9914 


0.3926 


8.9896 
0.9978 


0.4318 

86i 
0.0654 


1 


3° 
9986 


86i 
0.0610 


0.9981 


2 


1 9973 


0.1047 11.9968 


0.11.34 


11.9963 


0.1221 


1.9957 


0.1308 


3 


2 9959 


0.1570 12.9952 


0.1701 


2.9944 


0.1831 


2.9936;0.1962 1 


/I 


3.9945 


0.2093 


3.9935 


0.2268 


3.9926 


0.2242 


3.9914 0.2616 1 




4.9931 


0.2617 


4.9919 0.2835 


4.9907 


0.3052 


4.9893 


0.3270 


A 


5.9918 


0.3140 


5.9903|0.3402 


5.9888 


0.3663 


5.9871 


0.3924 




6.9904 


0.3664 


6.988810.3968 


6.986910.4273 


6.9860 


0.4578 


s 


7.9890 


0.41871 7.9871 0.4535 


7.9851 0.4884 


17.9829 


0.5232 


9 


8.9877 
E.W. 


0.4710':8.9855|0.5102 


9.9832 1 0.5494 


'8.9807 

e7w7 


0.5886 


N. S. 


lE.AY. 


IN. S. 


E.W. 


N. S. 


N. S. 



TABLES OF SURVEYS. 



181 



■l -^ , 




1 TABLES OF LATITUDE AND DEPARTURE. 






N. S. 


E.W. 


N. S. 


E.W. 


N. S. 


E.W. 


iN. S. |E. W. j 




1 


4° 


^86° 
0.0698 


4i 
0.9972 


85i 
0.0741 


44 
0.9969 


85i 
0.0784 


! 41" 
0.9965 


85i 
0.0828 




0.9976 




2 


1.9951 


).1395 


1.9945 


0.1482 


1.9938 


0.1569 


;1.9931 0.1656 




3 


2.9927 


0.2093 


2.9917! 


0.2223 


2.9907 


0.2364 


2.9897 0.2484 




4 


3.99021 


0.2790 


3.989010.2964 


,3.9977 


0.313813.986310.3312 | 




5 


4.9878 


0.3488 


4.9S62 0.3706 


4.9846 


0..3923; 4.9828 


0.4140 1 




fi' 5.9854 


0.4185 '5.983510.4446' I5.9S15 


0.4707 5.9794 


0.4968 




7|6.9829 


0.4883 ;6.9S07';0.5187 6.9784 0.5492; 6.9759 


0.5796 




8 


7.9805 


0.5580 i7.9780 0.5928 7.9753 0.6277; 17.9725 


0.6626 




9 

1 


8.9780 


0.6278 8.9752 


0.6670 


8.9722 


0.7061 8.9691 


0.7453 
0.1002 




5° 


85° ! 5i 
0.0871 0.9958 


84i 


1 5i 
0.9954 


84i 


6i 




0.9961 


0.0916 


0.0958 


0.9949 






1.9923 


0.1743! 1.9916 


0.1830 


1.9908 


0.1917 


1.9899 


0.2004 




3 


2.9884 


0.2615 ! 2.9874 


0.2745' 


2.9862 


0.2875 


2.9849 


0.3006 




4 


3.9846 


0.3486 3.9832 


0.3660 3.9816 


0.38.34 


3.9799 


0.4008 




5 


4.980S 


0.4358 


,4.979010.4575 14.9770 


0.4792 


4.9748 


0.5009 




6 


5.9769 


0.5229 


5.9748 0.5490 5.9724 


0.5761 


5.9698 


0.6011 




7 


6.9731 


0.6101 


16.9706 0.6405 6.9678 


0.6709 


6.9648 


0.7013 




8 


7.9692 


0.6972 


17.9664 0.7320 ,7.9632 


0.7668 


. 7.9597 


0.8016 




9 


8.9654 


0.7844 


8.9622 0.8235 


;8.9586 


0.8626 
8.3J 


8.9547 


0.9017 




6° 


84 


6i 83i 


6i 


1 61 


83i 




1 


0.9945 


0.1045 


0.9940 0.1088 '0.9935 


0.1132 


,0.9930 


0.1175 




2 


1.9890 


0.2090, 1.988l|0.2177|lL9871 


0.2264 


1 1.9861 


0.2351 




3 2.9836 


0.3136 


,2.9821 0.3266 |2.9807 


0.3396 


2.9792 


0.3526 




4 


3.9781 


G4181 


'3.9762 0.4355 13.9743 


0.4528 


3.9723 


0.4701 




5 


4.9726 


0.5226 


i4.9703 0.5443 


4.967810.6660 


|4.9653 


0.5877 




fi 


5.9671 


0.6272 


j 5.9643 


0.6532 


5.9614 0.6792 


5.9584 


0.7062 




716.9616 


0.7317 


6.9584 


0.7621 


6.9560 0.7924 


6.9515 


0.8228 




! 817.9562 


0.8362 


17.9524 


0.8709 


7.9486 0.9066 


7.9445 


0.9403 




9 


8.9507 
7° 


0.9408 
83° 


18.9465 

1 7i 


0.9798 


8.9421 


1.0188 


8.9376 
7i 


1.0678 

82i 




82i 


1 7i 


82i 




1 


0.9925 


0.1218 


0.9920 


0.12621 0.9914 


0.1306 


0.9908 


0.1348 




? 


1.9851 


0.2437 


1.9840 


0.2524, 1.9829 


0.2610 


1.9817 


0.2697 




3 


2.9776 


0.3656 


2.9760 


0.3786 2.9743 


0.3916 


2.9726 


0.4045 




4 


3.9702 


0.4874 


,.3.9680 


0.5048, 3.9657 


0.5221 


3.9635 


0.5394 




^ 


4.9627 


0.6093 


4.9600 0.6310 4.9572 


0.6626 


4.9543 


0.6742 




fi 


5.9553 


0.7312 


5.9520 


0.7572 5.9487 


0.7831i 15.9462 


0.8091 




7 


6.9478 


0.8531 


6.9440 


0.S834 6.9401 


0.9137] 6.9361 


0.9439 




8 


17.9404 


0.9750 


7.9360 


1.0096 7.9316 


1.0442 7.9269 


1.0788 




918.9329 


1.0968 


S.92S0 


1.13.58 8.9i30 


1.1747 8.9178 


1.2136 




L- 


1 E. W. 


N. S. 


E.W. 


N. S. 1 E.W. 'n. S. I E.W. 


NTs. 


J 



182 



THE surveyor's GUIDE. 



TABLES OF LATITUDE AND DEPARTURE. 




N. S. 


E.W. 


1 N. S. 


E. W.j 


N. S. 


E. W. iN. S. 


E. W. 


1 


8° 
(L99()2 


82 


1 8i 
0.9896 


811 
0.1435 


8i 
0.9890 


8H 
0.1478 


0.9883 


81^ 


0.1391 


0.1521 


2 


1.9805 


0.2783 


1.9793 


0.2870 


1.9780 


0.2956; 


1.9767 


0.3042 


3 


2.9708 0.4175 


2.9689 0.4305 


2.967010.4434112.9661 


0.4664 


4l3.961ll0.5567 


3.9586 0.5740' 


3.9560,0.6912 


3.9634 


0.6085 


5I4.9513 


0,6959 


4.9483]0.7176 


4.945110.7390 


4.9418 


0.7606 


6 


5.9416 


0.8350 


5.9379I0.86O5 


5.934110.8868 


6.9302 


0.9127 


7 


6.9319 


0.9742 


6.9276 1.0045 


6.9231! 1.0347 


6.9185 


1.0649 


8 


7.9221 


1.1134 


7.9172 


1.1479 7.9121]1.1826|.7.9069 


1.2170 


9 

1 


8.9124 


1.2626 


8.9069 


1.2914 


8.9011 


1.3303 


8.8952 
9S 


1.3691 


9° 


81 
07i664 


n 


80i 
0.1607 


n 


Tor 


0.9877 


0.9870 


0.9863'0.1650i 


0.9865 1 0.1 693 


2 


1.9754 


0.3129 


1.9740 


0.3216 


1.9726J0.3301, 


11.9711,0.3387 


3 


2.9631 


0.4693 


2.9610 


0.4822 


2.9689!0.4951 


|2.9566'0.6080 


4 


3.9508 


0.6267 


3.9480 


0.6430 


3.9451 


0.6602 


3.9422 


0.6774 


5 


4.9384 


0.7822 


4.9360 


0.S037 


4.9314 


0.8252 


4.9278 


0.8467 


6 


5.9261 


0.9386 


6.9220 


0.9644 


5.9177 


0.9903 


5.9133 


1.0161 




6.9138 


1.0950 


6.9090 


1.1252 


6.9040'1.1553l 


6.8989 


1.1864 


8 


7.9015 


1.2515 


7.8960 11.2869 


7.8903 


1.3204 


7.8844 


1.3648 


9 


8.8892 


1.4079 
80° 


8.8830 


1.4467 
79i 


8.8766 

,"ior 


1.4854 


8.8700 


1.6241 


10° 


1 lOi 


794 


m 


J9i_ 


1 


0.9848 


0.1736 


0.9840'0.1779 


1. 9832 j 0.1822 


0.9824 


0.1865 


2 


1.9696 


0.3473 


1.9681 10.3669 


0.9666 0.3045 


1.9649 0.3730 


3 


2.9544 


0.5209 


2.9521 


0.5338 


2.9497 0.5467 


2.9473 0.5596 


4 


3.9.392 


0.6946 


3.9362 


0.71181 3.9330;0.7289 


3.9298 0.7460 


5 


4.9240'0.8682 


4.9202 


0.8897 


4.9163 0.9112 


4.9123 0.9325 


6 


5.9088 


1.0419 


5.9042 


1.0676 


5.8995 1.0933 


6.8947,1.1190 


7 


6.8937 


1.21561 6.8S83 


1.2456 


6.882811.2756 


6.8772 1.3066 


8 


7.8785 


1.3892 


7.8723 


1.4235 


7.8660!l.4579 


7.8696 1.4920 


9 


8.8633 


1.6628 


8.8664 


1.6015 


8.8493 


1.6401 


8.8421 


1.6785 


1 


11° 
0.9816 


79 
0:i908 


~iu' 

0.9808 


7SS 


Hi 

0.9799 


78-r 

0.1993 


111 
0.9790 


78r 


0.1951 


0.2036 


2 


1.9633 


0.3816 


1.9616 


0.3902 


1.9598 


0.3987 


1.9581 0.4073 


3 


2.9449 


0.5724 


2.9424 


0.6863 


2.9398 


0.6981 


2.9371 0.6109 


4 


3.9265 


0.7632 


3.9231 


0.7804 


*3.9] 97 1,0.7976 


3.9162 0.8145 


5!4.9081 


0.9540 


4.9039'0.9765 


'4.8996 0.99(i,'- 


4.8952 1.0182 


616 8898 


1.1449 


5.884711.1705 


5.8796 i 1.1 962 


15.8743 1.2218 


716.8714 


1.3367 


6.8666 1 1.3666 


6.8596 1.3966 


16.8533 1.4265 


8 '7.853 3 


1.5266 


7.8463 1.6007 


7.8394 1.6949 


17.!- 324 1.6291 


1 9 1 8.8346 11. 71 73 


8.827l!l.7658 


8.8193J.7943I 8,8114 1.8327 

eTw? nTs'i Ie.~w; ¥.~s. 


I 1 eTw. I"n7^. 


E. W. N. S. 


u 



TABLES OF SURVEYS. 



183 



TABLES OP LATITUDE AND DEPARTURE. | 




N. S. 


E.W. 


N. S. ,E. W.I 


N. S. 


E. W. 


N. S. 


E. W. 




12° 


78° 


12i 1 77i 


12J 


77i 


m 


77i 


1 


0.9781 


0.2079 


0.9772 0.2122 


0.9763 


0.2164 


0.9753 


0.2207 


2 


1.95fi.S 


0.4158 


1.9544 0.4242 


1.9526 


0.4329 


1.9507 


0.4414 


3 


2.9344 


0.6237 


2.9317^0.6365 


2.9289 


0.6493 


2.9260 


0,6621 


4 


3.91^6 


0.8316 


3.9089 0.84871 


3.9052 


0.8657 


3.9014 


0.8828 


ft 


4.8907 


1,0396 


4.8861 


1.0609 


4.8815 


1.0822 


4.8767 


L1035 


6 


.5.8689 


1.2475 


5.8634 


1.2730 


5.8578 L2986I 


5.8520 


1.3242 


7 


fi.8470 


1.4554 


6.8406 


1.4852 


6.8341 


L5151||6.8274 


1.5449 


8 


7.8252 


1.6633 


7.8178 


1.6974 


7.8104 


1.7315 


7.8027 


L7656 


9 

1 


8.8033 
13° 


1.8712 

77° 
0.2249 


8.7951 
0.9734 


1.9096 


8.7867 


1.9479 
76i 


8.7781 

13i 

0.9713 


1.9863 1 

76i 
0.2377 


76i 


m 


0.9744 


0.2292 


0.9724 0.2334 


9. 


1.9487 


0.4499 


L9467 


0.4584 


1.9447 0.4669 


1.9427 


0.4764 


S 


?..9m 


0.6749 


2.9201 


0.68761 


2.9171 0.7003 


2.9140 


0.7131 


4 


3.8975 


0.8998 


3.8934 


0.91681 


3.8895 0.9338 


3.8864 


0.9507 , 


5 


4.8718 


1.1248 


4.8669 


1.1460 


4.8619 L1672 


4.8667 


L1884 


6 


.5.8462 


1.34971 i5.8403 


1.3752 


5.8343 1.4007 


16.8280 


1.4261 1 


7 


6.8206 


1.5746! 


6.8136 


1.6044 


6.8067 


L6341 


6.7994 


1.0638 


8 


7.7950 


L7996| 


7.7870 1.83361 


7.7790 


1.8676 


7.7707J 1.9015 !j 


9 


8.7693 


2.0246! 
76° 


8.7604 
14i 


2.0628 
75S 


8.7515 
14J 


2.1010 
75i 


8.7421 
14J 


2.1392 


14° 


I 1 


0.9703 


0.2419 


0.9692 


0.2461 


0.9681 


0.2604 


0.9670 


0.2546 


I ?. 


1.9406:0.4838 


L9385'0.4923 


L9363 


0.500S 


L9341 0.5092 1 


3 


2.91090.7258 


2.9077 0.7385 


2.9044'0.7511 


2.9011 0.7638 
3.86S2 1.1084 
4.8352 L2730 | 


4 


3.8812'0.9677 


3.8769 0.9846 


3.St27 1.0015 


5 


4.8515|l.2096 


4.8461 1.2308 


4.8407 


L2519 


fi 


5.8218 1.4515 


5.8154'L4769 


5.8089 


1.5023 


5.802311.5276 | 


7 


6.7921 1 1.6935 


6.7846 


1.7231 


6.7770 


L7627 


6.7693 1.7822 


8 


7.7624 1.9354 


7.7538 


1.9692 


7.7452 


2.0030 


7.7364 2.0368 1 


9 


8.7327, 2.1773| 


8.7231 
"l5i~ 


2.2154 

T4i~ 


8.7133 
15,^ 


2.2534 
"74^ 


8.7034 


2.2914 
74i 


15 


75 


15i 


1 


0.9659 


0.2588 


0.9648 


0.263O 


0.9636 


0.2672 


0.9624 


0.2714 1 


9. 


1.9319 


0.5176 


1.9296 


0.5261 


1.9273 


0.5345 


1.9249 


0.5429 i 


3 


2.8978 


0.7765, 


2.8944 


0.7891 


2.8909 


0.8017 


2.8874 


0.8143 , 


4 


3.8637 


1.0353 


3.8591 


1.0521 


3.854511.0689 


3.8498 


1.0858 


5 


4.8296 '1.29411 


4.8239 


1.3152 


4.8182 1.3362 


|4.8123|1.3572 1 


6 


5.7956|1,5529| 


5.7887 


1.5782 


5.7818 


L6034 


15.7747 11.6286 


7 


6.7615 


1.81171 


6.7535 


1.8412 


6.7454 


1.8707 


6.7372 1.9001 ! 


8 


7.7274 


2.0706 


7.7183 


2.1042 


7.7090 


2.1379 


7.6996 2.1715 jj 


9 


8.6933 


2.3294 


8.6831 

e"v~ 


2.3673 1 


8.6727 


2.4051 


8.6621 2 4430 


E.W. 


N. S. 


N.S.I 


E. VV. 


N. S. 


JE. W. 


N. S. Ij 



184 



THE SURVEYOR S GUIDE. 



TABLES OF LATITUDE AND DEPARTURE. | 




N.S. 
16° 


E. W. 

74 
0.2766 


N.S. 


E.W. 


N.S. 


E.W. 


N;S. 


E.W. 

73* 


16i 
0.9600 


731 

0.2798 


16i 

0.9588 


73i 
0.2840 


161 


0.9612 


0.9576 


0.2882 




L9225 0.5513 


1.9201 


0.5596 


1.9176 


).5680 


1.9151 


0.5764 




2.8838(0.8269 


2.8801 


0.8395 


2.8766 


0.8520 


2.8727 


0.8646 




3.8450 1.1025 


3.8402 


1.1193 


3.8353 


1.1361 


3.8303 


1.1528 




4.S063I 1.3782 


4.8002 


1.3991 


4.7941 


1.4201 


4.7878 


1.4410 |! 




5.767611.6638 


5.7603 


1.6790 


5.7629 


1.7041 


5.7454 


1.7292 j 




6.728811.9295 


6.7203 


1.9588' 


6.7117 


1.9881 


6.7030 


2.0174 1 




7.6901 


2.2051 


7.6804 


2.2386 


7.6705 


2.2721 


7.6606 


2.3066 


1 


8.6513 


2.4807 
73 


8.6404 

17i 
0.9550 


2.5185 
0.2965 


8.6294 

m 

0.9537 


2.6561 


8.6181 

171 

0.9523 


2.5938 
72i 
0.3048 


17 


0.9563 


0.2924 


0.3007 




1.9126 


0.5847 


1.9100 


0.5931 


1.9074 


0.6014 


1.9048 


0.6097 : 




2.8689 


0.8771 


2.8651 


0.8896 


'2.8611 


0.9021 


2.8572 


0.9U6 




3.8252 


1.1695 


.3.8201 


1.1862 


3.8149 


1.2028 


3.8096 


1.2195 




4.7815 


1.4619 


4.7761 


1.4827 


14.7686 


1.5035 


4.7620 


1.524.? 




5.7378 


1.7642 


5.7301 


1.7792 


1 5.7223 


1.8042 


5.7144 


1,8292 1 




6.6941 


2.0466 


6.6851 


2.0758 


16.6760 


2.1049 


6.6668 


2.1340 ' 




7.650412.3390' 


7.6402 


2.3723 


7.6297 


2.4066 


7.6192 


2.4389 , 




8.6067 
18° 


2.6313 

72 


8.5962 


2.6689 


8.6834 


2.7063 
7H 


8.5716 
~^8f 


2.7438 
7U 


711 


18i 




0.9510i 0.3090 


0.9497 


0.3131 


0.9483 0.3173 


0.9469'0.3214 1 




1.9021 0.6180 


1.8994 


0.6263 


1.8966 0.6346 


1.8939,0.6429 J 




2.8532 0.9271 


2.8491 


0.9395 


2.8450 0.9519 


2.8408 


0.9613 • 




3.8042 1.2361 


3.7988 


1.2527 


3.7933 1.2692 


3.7877 


1.2857 i 




4.7553 


L6451 


4.7485 


1.5658 


4.7416 1.6865 


4.7346 


1.6072 i 




5.7063 


1.8541 


5.6982 


1.8790 


5.6899 


1.9038 


6.6816' 1.9286 | 




6.6574 


2.1631 


6.6479 


2.1921 


6.6383 


2.2211 


6.6286 2.2601 




7.6084 


2.4721 


7.6976 


2.5053 


7.6866 


2.5384 


7.5754 2.5715 




8.5595 


2.7812 


8.5473 


2. 8186 


8.5349 


2.8567 


8.5224 2.S929 




19= 
0.9455 


71° 
0.3255 


19i 


70i 
0.3297 


19i 
0.9426 


70i 
0.3338 


191 70i 
0.9412 0.3379 


0.9441 




1.S91U 


0.6511 


1.8882 


0.6594 


1.8853 


0.6676 


1.8823:0.6758 




2.8366 


0.9767 


2.8323 


0.9891 


2.8279 


1.0014 


2.8233 1.0137 




3.7821 


1.3023 


3.7764 


1.3188 


3.7706 


1.3352 


3.76471.3517 




4.7276 


16278 


4.7204 


1.6484 


4.7132 


1.6690 


4.7059jl,6896 




5.6731 


1.9534 


5.6645 


1.9781 


6.6558 


2.0028 


5.6471 [2.0276 




6.6186 


2.2700 


6.6086 


2.3078 


6.5986 


2.3366 


6.588212.3654 




7.5641 


2.6045 


7.6527|2.0375 


7.6411 


2.6705 


7.6294 2.7033 1 




8.5097 


2.9301 


8.496812.9672 


8.4838 


.3.0043 


8.4706 3.0412 


;_ 


E. W. 


N. S. 


e.w.In. s. 


E.W.I N.S. 


1 E.W.! N.S. 



TABLES OF SURVEYS. 



185 





TABLES OF LATITUDE 


AND 


DEPARTURE 






N. S. 


B.W. 

70 


N. S. 
20i 


E. AV. 


N. S. 
20i 


E. W. 

~69r 


N. S. 


E. W. 


20 


691 


69i 


1 


0.9397 


0.3420 


0.9382 


0.3461 


0.9366 0.3502 


0.9351 


0.3543 


2 


1.8794 


0.6840 


1.8764 


0.6922 


1.8733 0.7004 


1.8703 


0.7086 


3 


2.8191 


L0261 


2.8146 


1.0383 


2.8100 1.0606 


•2.8064 


1.0629 


4 


3.7588 


1.3681 


3.7628 


1.3845 


3.7467.|l.4008 
4.6834ll.7510 


3.7406 


1.4172 


6 


4.6985 


1.7101 


4.6910 


1.7306 


4.6767 


L7715 


6 


5.6381 


2.0521 


5.6291 


2.0767 


5.6200 


2.1012 


6.6108 


2.1267 


7 


6.5778 


2.3941 


6.5673 


2.4228 


6.6567 


2.4514 


6.6459 


2.4800 


« 


7.5175 


2.7362 


'..5055 


2.7689 


7.4934 


2.8016 


7.4811 


2.8343 


9 

1 


8.4572 
21° 


3.0782 


A4437 3.1160 
1 21i 68i 
i0.9320 0.3624 


8.4300 

_2H 
0.9304 


3.1519 


8.4162,3.1886 


69° 


m 


21 i m 


0.9336 


0.358'l 


0.3666 


0.9288|0.3705 


2 


1.8672 


0.7m(il.8640 


0.7249 


1.8608 


0.7330 


1.867610.7411 


3 


2.8008 


1.P757!, 2.7960 


1.0873 


2.7913 


'1.0996 


2.7864|L1117 


4 


3.7343 


1.433r 1 13.7280 


1.4497 


3.7217 


1.4660 


3.7152 1.4822 


5 


4.6679 


L79181 


|4.6600 


1.8122 


4.6621 


1.8325 


4.6440 L8528 


6 


5.6015 


2.1502 


5.5920 


2.1746 


5.5826 


2.1990 


5.5729 2.2233 


7 


6.5351 


2.6086 


6.6240 


2.5371 


6.5129I2.5665 


16.6017 2.5939 


8 


7.4686 


2.8669 


7.4660 


2.8995 i 


7.44332.9320 


7.43052.9644 


9 


8.4022 


3.2253 
68° 


8.3880 


3.2619 

67i" 


8.3738 3.2985 


8.3593 3.3360 


22° 


22J 


22i 


67i 


22i i 67i 


! 1 


0.9272 


0.3746 


0.9255! 0.3786 


0.9239 


0.3827i 0.922210.3867 


2 


1.8544 


0.7492 


L8511' 0.7573 


1.8478 


0.7664 1.84440.7734 


3 


2.7816 


1.1238 


2.7766|1.1359 


2.7716 


1.1480 12.7666 


1.1601 


4 


3.7087 


1.4984 


3.7022 


1.6146 


3.6966 


L5307 


3.6888 


1.5468 


5 


4.6359 


1.8730 


4.6277 


1.8932 


4.6194 


1.9134 


4.6110 


1.9335 


6 


5.5631 


2.2476 


5.6532 


2.2719 


6.6433 


2.2961 


5.6332 


2.3202 


7 


6.4903 


2.6222 


6.4788 


2.6506 


6.4671 


2.6788 


6.4654 


2.7069 


8 


7.4175 


2.9968 


7.4043 


3.0292 


7.3910'3.0615 


7.3776 


3.0936 


9 
1 


8.3447 


3.3715 

67 
0.3907 


8.3299 

23i 
0.9188 


3.4078 
66i 


8.3149 


3.4441 


8.2998 


3.4803 


23 


J3i 
0.9170 


66i 


23i 


66i 


0.9205 


0.3947 


0.3987 


10.9163 


0.4027 


2 


1.8410 


0.7816 


L8376 


0.7895 


1.8341 


0.7975 il.8306 


0.8065 


3 


2.7615 


1.1722 


2.7664 


1.1842 


2.7512 


L1962 


2.7459 1.2082 


4 


3.6820 1.6629 


3.6762 


1.6790 


3.6682 


L5950 


3.6612 1.6110 


S 


'4.6026,1.9537 


4.6939 


11.9737 


4.5863|1.9937 


4.5766 0.0137 


6 


1 6.5230 


2.3444 


6.5127 2.3686 


6.6024 2.3925 


5.4919 2.4165 


7 


6.4435 


2.7351 


6.4315 2.7632 


6.4194I2.7912 


6.4072|2.8192 


8 


7.364013.1268 


7.3503 3.1679 


7.3366 


.3.1900 


7.2225|3.2220 


9 


8.2845{3.5166 


8.2691 3.6527 


8.2635 


3.5887 


18.2378 3.6247 


! 


E. W. 


1 N. S. 


E. W 


1 N. S. 


E. W 


N. S. 


1 E. W 


!N. S. 



•_J 



186 



THE surveyor's GUIDE. 



TABLES OF LATITUDE AND DEPARTURE. j 




N. S. 
24 


E.W. 


N. S. 
24i 


E. W. 

65f" 


N. S. E. W.I 


N. S. 
241 


65i 1 


66 


24i 


65i 


1 


0.9135 


0.4067 


0.9117 


0.4107 


0.9099 


0.41471 


0.9081 


0.4186 


2 11.827] 


0.8135 


1.8235 


0.8214 


1.8199 0.82941 


1.8163 


0.8373 


3 12.7406 


1,2202 


2.7353 


1.2322 I2.7299|1.244l! 


2.7244 


1.2560 


4 


3.G542 1.62691 


3.6470.1.6429 


3.6398 L6588 


3.6326 


1.6746 1 


5 


4.5677 2.03371 


4.558812.0536 


4.5498 2.0735 


4.5407 


2.0933 1 


6 


5.4813 


2.4404 


5.470612.4643 


5.4598 2.4882 


5.4489 


2.5122 


7 


6.3948 


2.8472 


6.382312.8750 


6.369712.9029 


6.3570 


2.9306 


8 


7.30S4 


3.2539 


7.294113.2857 


7.2797|3.3175i 


7.2651 


3.3493 ! 


9 


8.2219 


3.6606 


8.2058 


3.6965 


8.1896 


3.7322 


18.1733 


3.7679 1 




25° 


65 


25i 


64i 


25i 


64.i 


25i 


64i || 


1 


0.9063 


0.4226 


0.9044 


0.4265 


0.9026 


0.4305 


0.9007 


0.4344 


2 


1.8126 


0.8452 


il.8089 


0.8531! 


1.8052 


0.8610 


1.8014 


0.8688 


3 


2.7189 


1.2679 


12.7134 1.2797! 


2.7077 


12915 


12.7021 


1.3032 


4 


3.6252 


1.6905 


j3.6178 


1.7063 


3.6103 


1.7220 


13.6028 


1.7376 i 


5 


4.5315 


2.1131 


4.5223 


2.1328 


4.5129 


2.1525 


14.5035 


2.1720 


6 


5.4378 


2.5357 


15.4267 


2.5594 


5.4155 


2.5831 


15.4042 


2.6004 


7 


6 3442 


2.9583 


6.3312|2.9860| 


6.3181:3.0136 


6.3049 


3.0408 


S 


7.2505 


3.3809 


7.2356 


3.4125 1 


7.2207 3.4441 


7.2056 


3.4752 


9 


8.1568 


3.8036 


8.1401 


3.83911 


8.12333.8746 


8.1063 


3.9096 




26° 


64° 


26.i 


63i 


26i 63i 


26i 


63i 


1 


0.8988 


0.4384 


0.8969,0.4423 


0.8949 0.4462 


0.8930 


0.4501 


2 


1.7976 


0.8767 


L7937 


0.8846 


1.7899 0.8924 


1.785910.9002 


8 


2.6964 


1.3151 


12.6906 


1.3269' 


2.6848, L33S6 


2.67891.3503 


4 


3.5952'l.7535 


13.5875 


L7692 


3.57971.7848 


3.5719 1.8004 




4.4940l2.1919 


1 4.4843 


2.2115 


4.4746 


2.2310 


4.4649 


2.2505 1 


fi 


5.3928 


2.6302 


1 5.3812 


2.6537 


5.3696 


2.6772 


5.3579 


2.7006 1 


7 


6.2916 


3.0686 


,6.2781 


3.0960 


6.2645 


3.1234 


6.2508 


3.1507 ( 


s 


7.1904 


3.5070i. 7.1750 


3.5383 


7.1594 


3.5696 


7.1438 


3.6008 ] 


9 


8.0891 


3.9453 


8.0718 


3.9806 


8.0544 


4.0158 


8.0368 


4.0509 1 




27° 


63 


27i 


62| 


27i 


62i 


271 


62i 


1 


0.89100.4540 


0.8890 


0.4578 0.8870 


0.4617 


0.8850 


0.4656 


?. 


1.7820 0.9080 


1.7780|0.9157 1.7740 


0.9235 


1.770010.9312 


.S 


2.6730;].3620 


2.6670!l.3736 2.6610|l.3852 


2.6650 1.3968 


4 


3.5640 1.8160 


3.5561 |l.S315 


3.54S0 


1.8470 


3.5400 


1.8624 J 


1 ■'' 


4.4550 2.2699 


4.445l!2.2894 


4.435(1 


2.3087 


|4.4250 


2.3281 


1 fi 


5 3460 12.7239 


5.3341 


2.7472 


! 5.3221 


2.7705 


15.3099 


2.7937 


1 7 


6.2370:3.1779 


6.2231 


3.2051 


16.2092 


3.2322 


6.1949 


3.2593 


s 


7.1280 3.6319 


7.1121 


3.6630 


[7.0961 


3.6940 


7.0799 


3.7249 


9 


8.0191 4.0859 


8.0011 


4.1209 


7.9831 


4.1553 


7.9649 


4.1905 1 




B. W. ' N. S. 


E. W.I N. S. 


E. \V. 


N. S. 


'e. av.In. s. 



TABLES OF SURVEYS. 



187 





TABLES OP LATITUDE AND 


DEPARTURE 


1 




N. S. 


E. W. 


N. S. 


E.W.I 


N.S. 


E. W. 


N.S. 


E.W. 




28 


62 
0.4694 


28i 
0.8809 


61i 


28^ 


61i 
0.4771 


28} 
0.8766 


6U 
0T48IO 


1 


0.8829 


0.4733 


0.8788 


2 


L7659 


0.9389 


1.7618 0.9466 


L7576 


0.9543 


1.7634 


0.9620 


3 


2.6488 


1.4084 


2.64271 1.4199 


2.6364 


1.4315 


2.6302 


1.443U ! 


4 


3.5318 


1.8779 


3.52361.8933 


3.5153 


1.90S6 


.3.5069 


1.9239 


5 


4.4147 


2.3474 


4.4045 3.3666 


4.3941 


2.3858 


4.3836 


2.4049 


6 


5.2977 


2.8168 


5.2S54I2.8399 


5.2729 


2.8629 


5.2604 


2.8859 


7 


6.1806 


3.2863 


6.1662 3.3132 


6.1517 


3.3401 


6.1371 


3.3669 


8 


7.0636 


3.75581 


7.0471 3.7866| 


7.0305 


3.8173 


7.0138 


3.8479 


v» 


7.9465 


4.2252 
61 


7.9280 4.2599 
29i 1 60i 


7.9093 
29,^ 


4.2944 
60i 


7.8905 
29i 


4.3289 1 




29 


1 


0.8746 


0.4848 


'0.8725J0.4886 


0.8703 


0.4924 


0.8682 


0.4962 


^ 


1.7492 0.96961 


,1.7450,0.9772 


1.7407 


0.9848 


L7364 


0.9924 


3 


2.6239 


1.45441 


2.617511.4659 


2.6111 


1.4773 


2.6046 


1.48S6 


4 


3.4985 


1.9392 


3.4900 1.9545 


3.4814 


L9697 


3.4728 


1.9849 





4.3731 


2.4240 


:4.3625 '2.4431 


4.3518 


2.4621 


4.3410 


2.4811 


fi 


5.2477 


2.9089 


■5.2350'2.9317l 


5.2221 


2.9545 


6.2092 


2.9773 


7 


6.1223 3.3937 


6.1075 3.4203 


6.0925 


3.4463 


6.0774 


3.4736 


S 


6.997013.8785 


6.9800 3.90901 


6.9628 


3.9394 


7.9466 


3.9697 


9 


7.8716 4.3633 


7.8525 4.3976 


7.8332 


4.4318 


7.S138 


4.4669 




30 60 


30i 59i 


30i 


59,^ 


30i 


59i 


1 


0.866010.5000 


0.8638 0.5038 


0.8616 


0.5075 


0.8594 


0.5113 


'>. 


1.7320 1.0000 


1.7277 1.0076 


1.7232 


1.0151 


1.7188 1.0226 


3 


2.5981 1.5000 


:2.59151.5]13 


2.5849 


1.5226 


2.5782 1.5339 


4!3.464ll2.2000 


I3.4552 2.0151 


3.4465 


2.0301 


3.4376 2.0462 


5 |4.3301 


2.5000 


4.3192 2.5189 


4.3081 


2.537Y 


4.2970 2.6564 


6 5.1961 


3.3000 


5.1830 3.0226 


5.1698'3.04o2 


5.1564 3.0677 


7 6.0622 


3.5000 


6.0468 3.5264 


[6.0314 


3.5528 


6.0158 3.6790 


8 6.9282 


4.0000 


6.9107 4.0302 


6.8930 


4.0603 


6.8762 


4.0903 


9 [7.7942 


4.5000 


7.7745 4.5339 


7.7547 


4.6678 


7.7346 


4.6016 


1 ^^ 


59 


3U 58i 


3U 


58.} 


311 


68i 1 


1 |0.8571 


0.5150 


0.8549 


0.5188 


0.8526 


0.5225 


: 0.8603 


0.5262 


2 11.7143 


1.0301 


1.7098 


1.0375 


1. 7053,1. OloO 


1.7007 


!l.0524 


3 12.5715 


1 5451 


2.5647^1.5563 


2.5579 


1.5675 


2.6510'1.6786 11 


4 3.4287 


2.0602 


3.4196 2.0751 


3.4106 


'2.0900 


3.4014 2.1048 1 
4.2618|2.6311 | 


5 4.2858 


2.5752 


4.2745 2.5939 


4.2632 


2.6125 


6 5.1430 


3.0902 


5.1295 


3.1126 


5.1158 


.3.1350 


5.1021 


3.1573 1 


7 


6 0002 


,3.6053 


5.9844 


3.6314 


5.9685 


3.6575 


5.9526 


3.6835 i 


s 


6.8573 


4.1203 


16.8393 


4.1602 


6.8211 


4.1800 


6.8028 


4.2097 


9 


7.7145 


4.6353 


7.6942 J4.66S9 


7.6738 


4.7025 


7.6532 


4.7359 


IeTw 


N. S. 


, E.W.I N.S. 


E.W. 


1 N.S. 


E.W.iN.ri. , 



188 



THE SURVEYOR S GUIDE. 



TABLES OF LATITUDE AND DEPARTURE. | 






N. S. 


E.W. 

58° 


N. S. 
32i 
0.8457 


E.W. 


N. S. 


E. W.l 

-m\ 

0.5373] 


N. S. 


E.W. 

"67i~ 




32° 


57i 
0.5336 


32i 
0.8434 


32« 




1 


9.8480 


0.5299 


0.8410 0.5409 




; 2 


L.6961 


1.0598 


1.6914 1.06721 


1.0868 


1.0746 


L6821 1.0819 




3 


2.5441 


1.5897 


2.537211.60081 


2.5302 1.6119 


2.6231 1.6229 




4 


i.3922 


2.1197 


3.3829 2.1344 


3.373612.1492 


3.3642 2.1639 




5 


4.2402 


2.6496 


4.228612.66^1 1 


4.2169 


2.6805 


4.2052 2.7049 


1 


(5 


5.0883 


3.1795, 


5.0744 


3.2017 


5.0603 


3 2238! 5.0462 3.2458 


I 


7| 


5.9363 3.70941 


5.9201 


3.7353 


5.9037 


3.76111 6.8873 


3.7868 


1 


« 


6.7S44 


4.2394 


6.7658 


4.2689 


6.7471 


4.2984 6.7283 


4.3278 




9 
1 


7.0324 
33 


4.7693 


7.6115 

33i 
0.8363 


4.8025 

5-6I 
0.5483 


7.5905 
8339 


4.8357 [7.5694 


4.8688 

56^ 
0.5555 




57 


56i 
0.5519 


33} 

0.8314 




0.838(5 


0.5446 




2 


1.0773 


1.0893 


1.6726 


1.0966 


1.6678 


1.1039 


1.6029 


1.1111 




3 


2.516U 


1.0339 


12.5089 


1.6449 


'2.5017 


1.65581 


2.4944 


1.6667 




4 


3.3547 


2.17843 


3.3451 


2.1932 


,3.3355 2.2077 


3.3259 


2.2223 




5 


4.1934 


2.7232 


4.1814'2.7415| 


4.1694 2.7597 


4.1573 


2.7778 




(i 


5.0320 


3.2678 


l5.0177|3.2898l 


5.0033 3.3116, 


4.9888 '3.3334 




7 


5,8707 


3.8125 


15.8510 3.8381 


5.8372 


3.8635 


5.8203.3.8890 




8 


0.7094 


4.3571 


1 0.6903 


4.3863 


6.6711 


4.4155 


6.6518 4.4446 


1 


9 


7.5480 


4.9018 


7.5200 


4.9340 


1 7.5059 


4.9074 


7.4832i5.0001 


1 




34 


56° 


34i 


5.5.i 


1 m 


55i 


343 551 


\ 


7 


0.82901 0^5692 


|o.8200 


0.5028 


'0.8241 0.56641 


0.8210 0.5700 


\ 


2 


L658ll].iis4 


1.6532 1.1250 


1.6482, 1.132N 


1.0433 1.1400 




1 -^ 


2.4871 l.fi770 


2.1798 


1.6884 


2.47241 1.0992 


2.4049 1.7100 




4 


3.3162 2.23(iS 


3.3063 


2.2512 


3.2965 '2.:i650 


3.2806 2. 2800 




ft 


4.1452|2.7900l 4.i:-i29 


2.8140 


4.1200,2.8320 


4.1082|2.8500 







4.0742!3.y,552| '4.9595 


3.3708 


4.9447 


3.3984 


4.9299 1 3.4200 




7 


5.8033 3.9144' 16.7861 


3 9390 


5.7689 


3.9048 


6.7615 3.9900 




8 


6.6323 


4.4735 


6.6127 


4.5024 


6.5930 


4.5313 


6.5732 1 4. 5(;00 




9 

1 


7.4013 
35° 


5.0327 


17.4393 
[ 35i 
0.8166 


5.0052 


7.4171 
"35"^ 
0.8141 


5.0977 

54i 
0.5807 


7.3948 1 6. 1300 
353 i 54i 


1 


55 


543 
0.5771 




8191 


0.5736 


0.8116 


0.5842 




?, 


1.638;' 


1.1472 


1.6333 


! 1.1543 


1.6282 


1.1014 


1.0231 


1.1685 




.S 


2.4575 


1.7207 


2.4499 


|l.7314ii2.4423 


1.7421 


2.4347 


1.7527 




1 ■* 


3.2766 


2.2943 


3.2606 2.3086 


3.2505 2.3228 


3.2463 2.3370 


' 


■ ft 


4.0958 


2.S679r4.0832,2.8857 


4.0700 


2.9035 


4.0579 2,0212 


' 


1 fi 


4.9149 3.1415 


4.8998 3.4629 


4.8847 


3.4842 


4.8694 3.5055 '. 


' 7 


5.7341 1.0150 


.5.7165 4.0400 


5.6988 


4.U049 


5.681 C 4,0897 | 
6.4926 14.6740 1 


8 


6.5532 4.5886 


0.533114.6172 


|6.5129 


4.6456 


1 ^ 


7.3724 5.1622 


7.3498 5.1943 


1 7.3270 


5.2263 


7.3042 '5.2388 

Erw.'iii.T' H 


1 lE. W.'N. S. 


K W. N. S. 


E. ^Y. 


i N. S. 



TABLES OF SURVEYS. 



189 



TABLES OF LATITUDE AND DEPARTURE. 1 




N. S. 


E.W. 


N. S. 


E.W. 


jN. S. E. W. 


IN. S. 


E. W. 




36 


54 


36i 


5.31 


1 36i m 


1 m 


5.3i 


I 1 


0.8090 


0.5878 


0.8064 


0.5913 


' 0.8038 0.5948 


osoia 


0.5983 


1 2 


1.6181 


1,1756 


1.6129 


1.1826 


1.6077,1.1890 


1.0-026 


1.1966 


1 3 


2.4271 1.7634 


2.4193 


1.7739 '2.4116 


1.7845 


2.4038 


1.7950 


4 


3.236l!2.3611 


3.2258 


2.3662 3.2154 


2.3793 


3.2050 


2.3933 


5 


4,0451 


2.9389 


4.0322 


2.9665 


4.0193 


2.9741 


4.0063 


2.9916 


6 


4.8541 


3.5267 


4.8387 


3.5478 


4.8231 '3.5689 


4.8075 


3.5899 


7 


5.6631 


4.1145 


5.6451 


4.1391 


5.6270 


4.1638 


6.6088 


4.1883 


8 


6.4721 


4.7023 


6.4516 


4.7304 


6.4308 


4.7586 


6.4100 


4.7866 


9 


7.2812 


5.2901 


7.2580 


5.3217 


7.2347 


6.3534 


7.2111 


5.3849 




37 


63 


37i 


52i 


37i 


52i 


37i 


m 


] 


0.7986 


0.6018 


] 0.7960 


0.605.3 


0.7933,0.6087 


0.7907 


0.6122 


2 


1.5973 


1.2036 


1.5920 


1.2106 


1.5867 


12176 


1.6814 


1.2244 


3 


2.3959 


1.8054 


'2.3880 


1.8159 


2.3801 


1.8263 


2.3721 


1.8366 


4 


3.1945 


2.4073, 


3.1840 


2.4212 


3.1734 


2.4360 


13.1628 


2.4489 


6 


3.9932 


3.0091 


3.9800 


3.0265 


3.966813.0438 


13.9534 


3.0611 


6 


4.7918 


3.6109 


4.7760 


3.6318 


4.7601 3.6626 


.4.7441 


3.6733 


7 


5.5904 


4.2127: 


15.6720 


4.2371 


0.5635 


4.2613 


5.5348 


4.2856 


8 


6 3891 


4.8145 


6.3680 


4.8424 


6.3468 


4.8701 


6.3255 4.8977 ! 


9 


7.1877 


5.4163 
52 


7.1640 


5.4476 
~61i~ 


7.1402 


6.4788 
51i 


7.1162 
381 


5.5099 
5U 




38° 


38i 


1 


0.7880 


0.6156 


0.7853 


0.6191 


0.7826 


0.6225 


0.7799 


0.6259 


2 


1.5760 


1.2313 


1.5706 


1.2382 


1.6652 


1.2450 


L6698 


1.2518 


3 


2.3640 


1.8470 


2.3559 


1.8673 


2.3478 


1.8675 


2.3397 


1.8778 


4 


3.1520 


2.4626 


3.1413 


2.4764 


3.1304:2.4900 


3.1195 


2.5037 


5 


3.9401 '3.0783! 


3.9266 


3.0965 


3.913013.1125 


3.8994 


3.1296 


6 


4.7281 


3.6940 


4.7119 


3.7146 


4.6966 3.7351 


4.6793 


3.7656 


7 


5.5161 


4.3096 


5.4972 


4.3337 


'6.478214.3576 


5.4592 


4.3815 


8 


6.3041 


4.9253 


6.2825 


4.9528 


6.2608 


4.9801 


6.2391 6.0074 1 


9 

1 


7.0921 


6.5409 j 

51 
0.62931 


7.0678 

"39r 

0.7744 


6.5718 

ToF 


7.0434 

39i 
0.7716 


6.6026 

502^ 
0.6361 


7.0190 

39i 

0.7688 


5.6333 1 

50i 
0.6394 


39° 


0.7771 


0.6327 


2 


1.5543 


1.25S6 


1.5488 


1.2664 


1.6432 


1.2621 


1.6377 


1.2789 


3 


2.. 33 14 


1.8880 


2.3232 


1.8981 


2.3149 


1.90821 


2.3065 


1.9183 


4 13.1086 


2.5173 


3.0976 


2.6308 


3.0865 2.6443 


3.0764 


2.5578 


5 


3.8857 


3.1466 


3.8719 3.16351 


3.8581 3.1804 


3.8442 


3.1972 1 


fi 


4.6629 


3.7759 


4.6463 


3.7962 


4.6297 


3.81651 


4.6130 


3.8366 1 


7 


5 4400 


4.4052 


5.4207 


4.4289 


6.4014 


4.45251 


5.3819 4.4761 | 


8 


6.2172 


5.0346 


6.1951 


5.0616 


6.1730 


6.08861 


6.1507 


5.1156 


9 


6.9943 


5.6639 


6.9695 


6.0943 


6.9446 


5.72471 


6.9196 


5.7550 


|E.W. 


N. S. 


kw. 


N. S. 


E. W. 


N. S. 1 


E. W. N. S. 1 



190 



THE SURVEYOK S GUIDE. 



TABLES OF LATITUDE AND DEPARTURE. | 


1 


N.S. 

40° 

0.7660 


E. W. 


N. S. 

40i 

0.7632 


E. W. 

49i 


N. S. 

40i 

0.7604 


E. W. 


N.S. 

40i 

0.7575 


E.W. 

49i 
0.6527 


50 

0.6428 


49 i 
0.6494 


0.6461 


2 


1.5321 


1.2856 


1.5265 


L2922 


1.5208 


1.2989 


1.5151 


1.3055 


3 


2.2981 


L9284 


2.2897 


1.9384 


'2.2812 


1.9483 


2.2727 


1.9583 


4; 3. 0642 


2.5711 


3.0529 


2.5845 


3.0416 


2.5978 


3.0303 


2.6110 


1 5 


3.8302 


3.2139 


J3.S162 


3.2306 


3.8020 


3.2472 


3.7878 


3.2638 


6 


4.5963 


.3.8567 


14.5794 


3.8767 


4.5624 


3.8967 


4.5454 


3.9166 


7 


5.3623 


4.4995 


5.3425 


4.5229 


,5.3228 


4.5461i 


5.3029 


4.5693 


8 


6.1284 


5.1423 


6.1059 


5.1690 


'6.0832 


5.1956! 


6.0605 


5.2221 


9 


6.8944 


5.7851 


6.8691 


5.8151 


6.8436 5.8450 


6.8181 


5.8748 




41 


49 


41i 


48i 


m 


48i 1 


41S 


48i 


1 


0.7547 


0.6560 


10.7518 


0.6593 


:0.7489 


0.6626 


0.7460 


0.6659 


2 


1.5094 


1.3121 


1.5037 


1.3187 


1.4979 


1.3252 


1.4921 


1.3318 


3 


2.2641 


1.9682 


2.2555 


1.9780 '2.2468 


1.9879' 


2.2382 


1.9976 


1 i 


3.0188 


2.6242 


3.0074 


2.6374 


2.9958 


2.65051 


2.9842 


2.6635 


i 5 


3.7735 


.3.2803 


3.7592 


3.2967 


,3.7447 


3.3131 


3.7303 


3.3294 


6 


4.5283 


3.9364 


4.5110 


3.9560 


! 4.4937 


3.9757 


14.4764 


3.9953 


7 '5.2830 


4.5924' '5.2629 


4.6I54' '5.2426 


4.6383 


5.2224 


4.6612 


8 ,6.0377 


5.2485. 6.0147 


5.2747] 5.9916 


5.3010 


5.9685 5.3270 !| 


9 6.7924 


5.9045 


'6.7666 


5.9341 


6.7405 


5.9636 


6.7145 


5.9929 




42 


48 


■m 


47i 


42. V 


47i 


421 


m 


1 


0.7431 


0.6691 


0.7402 


0.6723 


0.7373 


0.675<3 


0.7343 


0.6788 


2 


1.4863 


1.3383' 1.4804 


1.3147 1.4746 


1.3512 


1.4686 


1.3576 


3 '2.2294 


2.0074 


2.2207 


2.0171 2.2118 


2.0268 


2.2029 2.0364 


4 


2.9726 


2.6765 


2.9609 


2.6895 2.9491 


2.7024 


2.9373 2.7152 


5 


3.7157 


3.3457 


3.7011 


3.3618 3.6864 3.3779] 


3.6716 3.3940 


6 


4.45894.0148 


4.4413 


4.0342 4.4237 


4.0535 


4.4059 4.0728 1 


7 


5.2020 


4.6839 


5.1815 


4.7066 5.1610 


4.7291 


5.1402 4.7516 


8 15.9452 


5.3530 


5.9218 


5.3789, 5.8982 


5.4047 


5.8746 5.4304 


9! 6.6883 


6.0222 


6.6620 


6.0513 


6.6355 


6.0803 


6.6089 6.1092 


1 ^^ 


47 


1 m 


461 


43i 


46i 


43S 


46i 


1 0.7313 


O.6S20I '0.7283 


0.6852 


0.7253' 0.68S3| 


0.7223 


0.6915 


2 !l.4627 


1.3640 


1.4567 


1.3704 


1.4507 


1.3767 


1.4447 


1.3830 


a 2.1941 


2.0460 


2.1851 


2.0555' 2.1761 


2.0651 


2.1671 


2.0745 


4 2.9254 


2.7280 


2.9135 2.7407 2.9015 


2.7534 


2.8894l2.766« || 


5 3.6568 


3.4100 


3.6418 3.4259 


13.6269 


3.4418 


3.6118 


3.4576 


i 6 14.3881 


4.0920 


4.3702 


4.1111 


I4.3522 


4.1301 


4.3342 


4.1491 ! 


1 7 5.1195 


4.7740 


5.0986 


4.7963 


5.0776 


4.8185 


5.0565 


4.8406 i 


8 6.8508 


5.4560 


5.8269 


5.4814 


I5.8O3O 


5.5068 


5.7789 


5.5321 1 


9 6.5822 


6.1380 


6.5553 


6.1666 


'6.5284 


6.1952 


6.5013 


6.2236 


1 1 E. W. 


N. S. 1 E. W. 


N. S. 


E. W. 


N. S. 


E.W. 


N.S. 1 



TABLES OF SURVEYS. 



191 



TABLES OF LATITUDE AND DEPARTURE 






N. S. 


E.W.I N. S. 


E. W. 


N. S. 1 E. W. 


N. S. 


E. W. 




44° 


46 Uk 


453 


44i Abh 


445 


~45r 


1 


0.7193'0.6946i 0.7163 


0.6978 


0.7132,0.7009 


0.7102 


0.7040 


'2. 


L4387iL3893| L4326 


1.3956 


i 1.4265 


).401S 


! 1.4204 


1.4080 


a 


2.1580 2.0840' 


2.14S9 2.0934 


2.1397 


2.1027 


2.1305 


2.1120 


4 


2.8774,2.7786, 


2.8652 


2.7912 


2.8530.2.8036 


|2.8407 


2.8101 


;> 


3.5967 


3.4733 


3.5815 


3.4889 


3.5662 


3.5045 


,3.5509 


3..5201 


6 


4.3160 


4.1679 


4.2978 


4.1867 


4.2795 


4.2054 


4.2611 


4.2241 1 


V 


5.0354 


4.8626 


5.0141 


4.8845 


4.9927 


4.9063 


4.9713 


4.9281 


s 


5.7547 


5.5573 


5.7304 


5.5823 


5.7060 


5.6072 


5.6S15 


6.6321 


1 


6.4741 
45 


6.2519 


6.4467 


6.2801 


6.41.92 


6.30«1 


6.3917 


6.3361 


45 
0.7071 








07071 


2 


1.4142 


1.4142 














3 


2.121312.1213 














4 


2.82842.82S4 

















3.5355'3.5355 














6 


4.2426 4.2426 














7 


4.9497 4.9497 
5.6569 5.6569 














8 














9 


6.3640 6.3640 
















E W. N. S. 


1 E. W. 


N. S. 


E.W. 


N. S. 


E.W. 


KS. 



TABLES OF SURVEYS. 



THE USE OF THE FOREGOING TABLES IN RELATION 
TO SURVEYS. 

They show, by inspection, the alteration of lati- 
tude and departure to every degree on the com- 
pass, and that for any distance not exceeding 
100.000 links. 

In the uppermost rank of every division are 
placed the several angles and their complements, 
to 45°, including the quarter, half, and three- 
quarters of degrees ; and in the left-hand column 
are lengths of the measured lines of the field- 
work, and in the common areas are the difference 
of latitude and departure. 

Examples. 
Suppose the angle to be N. E. 27J degrees, and 
the line in the field measured to 6 chains, and 
it be required to find the Northings and Eastings 
of that station, under 27|^ degrees, and answering 
to 6 in left-hand column, the number in the com- 
(193) 



TABLES OF SURVEYS. 193 

nion area, 5.3221, which shows the Northings ; 
and under 62J, (which is the complement to that 
angle) opposite the same number in the side col- 
umn, I find 2.7705, which shows the Easting of 
that station. If the course be the same, and dis- 
tance 60 chains, remove the decimal point one 
place to the right-hand, and the latitude and de- 
parture will be 53.221 27,705. 

And if the line were 600 chains, the course 
remaining the same, the Northings would be 532 
chains, 21 links, and the Eastings 277 chains, 05 
links. 

If the measured line doth not consist of an ex- 
act number of tens, as suppose its length to be 75 
chains, 03 links, or 75 chains, 34 links, and the 
course 27J° ; then under this angle, and opposite 



c. 

70 are 


62.091 




.32.322 


5 " 


4.435 


5 " 


2.308 


0.30 links 


0.266 


0.30 links 

0.04 " 


0.138 


0.04 " 


0.035 


0.018 


NorthinsT 


66.827 


Eastinf 


34.786 



for 76 chains, 34 links. for 75 cliains, 34 links. 

And so for any other. 

N. B. These tables will answer to ^° or 7|', an 
arithmetical mean between J° and J°, or between 
r and f °. 
13 



SYSTEMS OF RECTANGULAll SUE- 

VEYING FOR SURVEYING THE 

PUBLIC LANDS OF THE 

UNITED STATES.* 

The public lands of the United States are ordi- 
narily surveyed into rectangular tracts, bounded 
by lines conforming to the cardinal points. This 
is effected by meridian lines and parallels of lati- 
tude, established six miles apart. The squares 
thus formed are called townships. They are 
bodies of land 6 miles square, as near as may be, 
containing as near as may be 23,040 acres. The 
townships are subdivided into 36 tracts, called sec- 
tions, each containing as near as may be 640 acres. 
Any number or series of contiguous townships, sit- 
uate north or south of each other, constitute a 
range . 

*This section is mainly taken from "Manual of Sur- 
veying Instructions for the Survey of the Public Lands 
of the United Sates and Private Land Claims, Washrng- 

tou, 1890." 

(194) 



SURVEYING THE PUBLIC LANDS. 195 

The law requires that the lines of the public 
surveys shall be governed by the true meridian, 
and that the townships shall be six miles square — 
two things involving in connection a mathematical 
impossibility — for, strictly to conform to the meri- 
dian, necessarily throws the township out of square 
by reason of the convergency of meridians, and 
hence, by adhering to the true meridian, results 
the necessity of departing from the strict require- 
ments of law as respects the precise area of town- 
ships and the subdivisional parts thereof, the town- 
ships assuming something of a trapezoidal form, 
which inequality develops itself more and more as 
such, the higher the latitude of the surveys. In 
view of these circumstances the law provides that the 
sections of a mile square shall contain the quantity 
of 640 acres, as nearly as may he., and moreover 
provides that in all cases where the exterior lines 
of the townships, thus to be subdivided into sections 
or half sections, shall exceed or shall not extend 6 
miles, the excess or deficiency shall be especially 
noted, and added to or deducted from the western 
or northern ranges of sections or half sections in 
such townships, according as the error may be in 



196 THE surveyor's guide. 

running the lines from east to west, or from south 
to north ; the sections and half sections bounded on 
the northern and western lines of such townships 
shall be sold as containing only the quantity ex- 
pressed in the returns and plats, respectively, and 
all others as containing the complete legal quantity. 

Standard parallels are established at intervals of 
every 24 miles, north and south of the base line, and* 
guide meridians at intervals of every 24 miles, east 
and west of the principal meridian ; the object being 
to confine the errors resulting from convergence of 
meridians and inaccuracies in measurements, within 
the tracts of lands bounded by the lines so estab- 
lished. 

The survey of all principal base and meridian, 
standard parallels and guide meridians and town- 
ship lines, must be made with an instrument ope- 
rating independently of the magnetic needle. 
Burt's improved solar compass, or other instru- 
ment of equal utility, must be used of necessity in 
such cases ; and it is deemed best that such instru- 
ment should be used under all circumstances. 
Where the needle can be relied on, however, the 
ordinary compass, if provided with a revolving 



SURVEYING THE PUBLIC LANDS. 197 

compass box and variation arc, may be used in sub- 
dividing and meandering. 

The township lines and the subdivision lines will 
usually be measured by a two-pole chain of 33 feet 
in length, consisting of 50 links, and each link being 
seven and ninety-two-hundredths of an inch long. 
On uniform and level ground, however, the four- 
pole chain may be used. The measurements will, 
however, always be represented according to the 
four-pole cTiain of 100 links. 

Tally-pins. Eleven tally-pins made of steel are 
to be used. They should not exceed 14 inches in 
length, be weighty enough toward the point to make 
them drop perpendicularly, and have a ring at the 
top, in which is to be fixed a piece of red cloth, or 
something else of conspicuous color to make them 
readily seen when stuck in the ground. 

Process of chaining. In measuring lines with 
a two-pole chain, every five chains are called a 
" tally ;" and in measuring lines with a four-pole 
chain every ten chains are called a tally, because 
at that distance the last of the ten tally-pins with 
which the forward chainman sets ont will have 
been stuck. He then cries " tally," which cry is 



198 THE surveyor's guide. 

repeated by the other chainman, and each registers 
the distance by slipping a thimble, button or ring 
of leather, or something of the kind, on a belt worn 
for that purpose, or by some other convenient 
method. The hind chainman then comes up, and 
having counted, in the presence of his fellow, the 
tally-pins which he has taken up, so that both may 
be assured that none of the pins have been lost, he 
then takes the forward end of the chain and pro- 
ceeds to set the pins. Thus the chainmen alter- 
nately change places, each setting the pins that he 
has taken up, so that one is forward in all the odd, 
and the other in all the even tallies. Such proce 
dure, it is believed, tends to assure accuracy ia 
measurement, facilitates the recollection of the dis.- 
tances to objects on the line, and renders a, mis- 
tally almost impossible. 

Levelling the chain and 'plumbing the pins. 
The length of every line run is to be ascertained 
by precise horizontal measurements,, as nearly ap- 
proximating to an air-line as is possible in practice 
on the earth's surface. This all-important object 
can only be attained by a rigid adherence to the 
three following observances : 



SURVEYING THE PUBLIC LANDS. 199 

1. Ever keeping the chain stretched to its ut- 
most degree of tension on even ground. 

2. On even ground, keeping the chain not only- 
stretched as aforesaid, but horizontally levelled. 
And when ascending or descending steep ground, 
hills or mountains, the chain will have to be short- 
ened to one-half its length (and sometimes more), 
in order accurately to obtain the true horizontal 
measure. 

3. The careful plumbing of the tally pins, so as 
to ascertain precisely the spot where they should 
be stuck. The more uneven the surface, the 
greater the caution needed to set the pins. 

Marking lines. All lines on which are to be 
established the legal corner boundaries are to be 
marked after this method, viz : Those trees which 
may intercept your line must have two chops or 
notches cut on each side of them without any other 
marks whatever. These are called " sight-trees''' or 
" line-trees^ A sufficient number of other trees 
standing; nearest to your line, on either side of it, 
are to be blazed, on two sides diagonally or quarter- 
ing toward the line, in order to render the line 
conspicuous and readily to be traced, the blazes 



200 THE surveyor's guide. 

to be opposite each other, coinciding in direction 
with the line where the trees stand very near it, 
and to approach nearer each other the further the 
line passes from the blazed trees. Due care must 
ever be taken to have the lines so well marked as 
to be readily followed, and to cut the blazes' deep 
enough to leave recognizable scars as long as the 
trees stand. 

Bushes on or near the line should be bent at 
right angles therewith, and receive a blow of the 
axe at about the usual height of blazes from the 
ground, sufficient to leave them in a bent position, 
but not to prevent their growth. 

On trial or random lines, the trees are not to 
be blazed, unless occasionally from indispensable 
necessity, and then it must be done so guardedly as 
to prevent the possibility of confounding the marks 
of the trial line with the true. But bushes and 
limbs of trees may be lopped, and stakes set on the 
trial or random line, at every ten chains, to enable 
the surveyor on his return to follow and correct the 
trial lines and establish therefrom the true line. 
To prevent confusion, tne temporary stakes set on 
the trial or random lines must be pulled when the 
surveyor returns to establish the true line. 



SURVEYING THE PUBLIC LANDS. 201 

EstahlisMng corners. After a true coursing 
and most exact measurements the establishment of 
corners is the consummation of the work. If, there- 
fore, the corner be not perpetuated in a permanent 
and workmanlike manner, the great aim of the sur- 
veying service wilL not have been attained. A 
boundary corner, in a timbered country, is to be a 
tree, if one be found at the precise spot ; and if 
not, a post is to be planted thereat ; and the posi- 
tion of the corner-post is to be indicated by trees 
adjacent (called bearing trees), the angular bear- 
ings and distances of which, from the corner, are 
facts to be ascertained and registered in the field- 
book. 

In a region where stone abounds, the corner 
boundary will be a small monument of stones along- 
side of a single marked stone, for a township cor- 
ner — and a single stone for all other corners. 

In a region where timber is not near, nor stone, 
the corner will be a mound of earth, of prescribed 
size, varying to suit th.e case. 

The following are the different points for perpet- 
uating corners, viz : 

1. For township boundaries, at intervals of every 
six miles. 



202 THE surveyor's guide. 

2. For section boundaries, at intervals of every 
mile, or eighty chains. 

3. For quarter section boundaries, at intervals 
of every half mile, or 40 chains. 

4. Meander corners are established at all those 
points where the lines of the public surveys inter- 
sect the banks of such rivers, bayous, lakes or 
islands as are by law directed to be meandered. 

Meandering is a term applied to the usual mode 
of surveying with the compass, particularly as ap- 
plied to navigable streams. The instructions for 
this are, in part, as follows : 

Both banks of navigable rivers, as well as all 
rivers not embraced in the class denominated as 
" navigable," the right-angle width of which is 
three chains and upwards, will be meandered by 
taking the courses and distances of their sinuosities, 
and the same are to be entered in the field book. 
At those points where either the township or sec- 
tion lines intersect the banks of a navigable stream 
or any meanderable line, corners are to be estab- 
lished at the time of running these lines. These are 
called "meander corners ;" and in meandering you 
are to commence at one of those corners, coursing 



SURVEYING THE PUBLIC LANDS. 203 

the banks or boundary line, and measuring the dis- 
tance of each course from your commencing corner 
to the next " meander corner." By the same 
method you are to meander the opposite bank of 
the river. 

The crossing distance between the meander cor- 
ners^ on the same line, and the true bearing and 
distance between opposite meander corners is to be 
ascertained by triangulation or direct measurement, 
in order that the river may be protracted with entire 
accuracy. The particulars to be given in the field- 
notes. 

You are also to meander, in manner aforesaid, 
all lakes and deep ponds of the area of 25 acres 
and upwards ; also navigable bayous. The precise 
relative position of islands in a township made frac- 
tional by the river in which the same are situated, 
is to be determined trigonometrically. Sighting 
to a flag or other fixed object on the island from a 
special and carefully measured base-line, con- 
nected with the surveyed lines, on or near the 
river bank, you are to form connection between the 
meander corners on the river to points correspond- 
ing thereto, in direct line, on the bank of the 



204 THE surveyor's guide. 

island, and there establish the proper meander cor- 
ners, and calculate the distance across. 

Surveying. The initial point having been 
established, the lines of the public survey are to 
be extended therefrom as follows : 

Base line. The base line shall be extended east 
and west from the. initial point by the use of solar 
instruments or transits. The transit should be desig- 
nated for the alignment of all important lines. The 
proper corners shall be established at each 40 and 
80 chains, and at the intersection of the line with 
rivers, lakes, or bayous that should be meandered, 
in accordance with the instructions for the estab- 
lishment of corners. In order to check errors in 
measurement, two sets of chainmen, operating inde- 
pendently of each other, must be employed. 

Where transits are used, the line will be run by 
setting off at the point of departure on the principal 
meridian a tangent to the parallel of latitude, which 
will be a line falling at right angles to said meridian. 
The line thus determined will be prolonged by two 
back and two fore sights at each setting of the instru- 
ment, turning the horizontal limb 180° in azimuth 
between the observations. The survey will be con- 



SURVEYING THE PUBLIC LANDS. 205 

tinued on this line for 12 miles, but the corners 
■will be established at the proper points by ofF-sets 
northerly from said line, at the end of each half 
mile. 

Principal meridian. The principal meridian 
shall be extended north and south from the initial 
point, by the use of solar instruments or transits. 
Where solar instruments are used, the line will be 
run in the same manner as prescribed for running 
the base line by solar instruments. Where transits 
are used, observations upon the polar star must be 
taken within each 12 miles of line run. Two sets 
of chainmen operating independently of each other 
must be employed. 

Standard parallels. Standard parallels which 
are also called correction lines, shall be extended 
east and west from the principal meridian, at inter- 
vals of every 21 miles north and south of the base 
line, in the same manner as prescribed for running 
the base line. 

Guide meridians shall be extended north and 
south from the base line at intervals of every 21 
miles east and west from the principal meridian, in 
the same manner as prescribed for running the 
principal meridian. 



206 THE surveyor's guide. 

Exterior of township lines. The east and west 
boundaries of townships are always to be run from 
south to north on a true meridian line ; and the 
north and south boundaries are to be run from east 
to west, or from west to east, on a random or trial 
line, and corrected back to a true line. The dis- 
tance north or south of the township, corner to be 
closed upon, from the point of intersection of these 
random lines with the east or west boundary of the 
township, must be carefully measured and noted. 
Should it happen, however, that such random line 
should fall short, or overrun in length, or intersect 
the east or west boundary more than three chains^ 
distance from the township corner thereon, as 
compared with the corresponding boundary on 
the south (due allowance being made for con- 
vergency) the line, and if necessary the entire 
exterior boundaries of the township, must be 
retraced, so as to discover and correct the 
error. In running random lines, temporary cor- 
ners are to be set at each 40 and 80 chains, and 
permanent corners established upon the true line 
as corrected back, in accordance with instructions, 
throwing the excess or deficiency on the west 



SURVEYING THE PUBLIC LANDS. 207 

half as prescribed by law. Permanent corners are 
to be established in accordance with instructions 
on the east and west township boundaries at the 
the time they are run. Whenever practicable, the 
township lines within these tracts of 24 miles 
miles square must be surveyed in regular order 
from south to north, i. e., the exterior boundaries 
of the township in any one range lying immediately 
north of the south boundary of such tract of 24 
miles square must first be surveyed, and the exte- 
riors of the other three townships in said range 
extended therefrom in regular order from south to 
north, and it is preferable to first survey the 
entire range of townships in such tract adjoining 
the east boundary or the west boundary, and the 
other three ranges in regalar sequence. In cases, 
however, where the character of the land is such 
that this rule cannot be complied with, the following 
will be observed : 

In extending the south or north boundaries of a 
township to the west, where the southwest or north- 
west corners cannot be established in the regular 
way by running a north and south line, such boun- 
daries will be run west on a true line, allowing; for 



208 THE surveyor's guide. 

convergency on the west half mile ; and from the 
township corner established at the end of such 
boundary,, the west boundary will be run north or 
south as the case may be. In extending south or 
north boundaries of a township to the east, where 
the southeast or northeast corner cannot be estab- 
lished in the regular way, the same rule will be 
observed, except that such boundaries will be run 
east on a true line, and the east boundary run 
north or south, as the case may be. 



Il^DEX. 



ACRE, content of the, 42 
Angle-mirror, its construc- 
tion and mode of op- 
eration, 53-58 
Angle-mirror, testing, the, 64, 65 
to erect a perpendicular 
with the assistance of 
the, 59, 60 
to find an intermediate 
point in a straight 
line, with the assist- 
ance of the, 62-64 
to let fall a perpendicu- 
lar, with the assist- 
ance of the, 60-62 
use of the, 58, 59 
Angle of incidence, 55 
reflection, 55 
to determine the, made by 
two stations of a survey, 
136-143 
Angles, right, examples of the 
application of setting 
out, 69-75 
instruments for setting 

out, 46-75 
prism for, and its use, 

65, 66 
to set out with the 
tape-measure, 67-69 
Areas, 82-106 
Axis of incidence, 55 

(2 



BASE line, the, of the public 
survey, 204, 205 
Blazing, 199 
Boundary corner, 201 

stones, 20 
Burt's improved solar compass, 



CALCULATION, methods of, 
141-143 
Calculation, new method of, 144- 
147 
Noble's method of, 147-153 
Chain, levelling the, and plumb- 
ing the pins, 198, 199 
Chaining, process of, 197-199 
Chains, 39-41 

Grumman's patent, 40, 41 
metre, 41 
vara, 41 
Circle, to find the area of a, 105 
Cities, posts used, in taking 

measurements in, 20, 21 
Compass, to survey with the, 

through any mine, 153, 154 
Corner, boundary, 201 
Corners, establishment of, 201,202 
points for perpetuating, 201 
202 
Cross statf-head, and its use, 47- 
51 
testing the, 51-53 

9) 



210 



INDEX. 



Cross staff-head, or surveyor's 
cross, and its use, 46- 
51 

Curves on railroads, to inflect in, 
168-179 

DEPARTURE and latitude, 
tables of, 180-191 
Departure and latitude, to find 
the error in the difference of, 
120-126 
Distance, determination of a, 
when measuring is pre- 
vented by an obstacle, 
33-39 
example in measuring, 

133-135 
guessing or judging, 45 
to find the, when the 
straight line ;ontinues 
across a river, 36, 37 
Distances, instrument for finding, 
without calculation, 127- 
133 
instruments for measuring, 

and their use, 20-45 
various methods of meas- 
uring, 43-45 
Diurnal variation, mean, for every 
month in the year, 153 

ELLIPSIS, to find the area of 
an, 105 
Examples of the application of 
setting out right angles, 69-75 

FARM, triangular, division of a, 
97-99 
I'ield-book distances, measured 
with a 100 feet chain, 
165 



Field-book, methods of keeping, 

157-161 
Field, many-sided, to survey a, 
77-79 
or lot, to find the area of a, 
which is found to be the 
frustum or zone of a par- 
abola, 105, 106 
three-sided, to survey a, 76, 
77 
Forest, determination of the di- 
rection of a straight line 
through a, 38, 39 
or pond, to find the length 
when the straight line 
passes through a, 34-36 

GRUMMAN'S patent chains, 40, 
41 
Guide meridians, 205 
Gunter's link, 39 

INCIDENCE, angle of, 55 

j^ Incidence, axis of, 55 

Instrument for finding distances, 
without calculation, and 
its use, 127-133 
for measuring a map, 126, 
127 

Instruments for measuring dis- 
tances, and their use, 
20-45 
for setting out right angles, 
and their use, 46-75 

LAND, how to measure a tract 
of, by measuring a base-line 
through it, 115-120 
Land measurement, unit in, 42 
reduction of the content of a 
piece of, to acres, rods and 
perches, 42, 43 



INDEX. 



211 



Latitude and departure, tables of, 
180-191 
to find the error 
in the differ- 
ence of, 120- 
126 
Laying out or lotting towns, etc., 

156, 157 
Legs of stations, rules for altering 
the, in the correcting of sur- 
veys, 124-126 
Length, to find the, when the 
straight line passes through a 
pond or a forest, 34-36 
Levelling, 163-168 
Light, laws of the reflection of, by 

plane mirrors, 54 
Line, not horizontal, to measure 
a, with the measuring rods, 
29, 30 
straight, determination of a, 
18 
determination of the di- 
rection of a, through 
a forest, 38, 39 
establishment of a, 21 
length of a, 27 
measuring a, with the 
measuring rods, 28, 29 
to determine an inter- 
mediate point in a, 50,. 
51 
to determine a point in, 
a, when it is impossi- 
ble to take position in 
its prolongation, 25- 
27 
to erect a perpendicular 

at a point in a, 49 
tO) find an intermediate 
point in a, with the as- 
sistance of the angle- 
mirror, 62-64 



Line, straight, to find a point in 
a, 23-25 
to find a point in the 
prolongation of a, 21- 
23 
to let fall a perpendicu- 
lar to a, from a point, 
49, 50 
trees or sight trees, 199 
Lines, marking, 199, 200 

township, exterior of, 206- 

208 
trial or random, 200 
Lot or field, to find the area of a, 
which is found to be the frus- 
tum or zone of parabola, 105, 
106 
Lotting or laying out towns, etc., 
156, 157 

MAP, instrument for.measUjriag 
a, 126, 127 
Marking lines, 199, 200.^ 

pins, 32, 41, 42 
Meander corners,. 202 
Meandering,, definition of, 202 

instruction for, 202-204 
Mearings,. tracing of old, 161-163 
Measure, tape, and its appurten- 
ances, 3.0, 31 
Measurements, noting the results 

of the, 79, 80 
Measuring distances, various 
methods of, 43-45 
rods, and their use, 28-30 
Meridian, principal, 205 
Meridians, guide, 205 
Metre chains, 41 
Mile, square, content of a, 42 
Mine, to survey with the compass 

through any, 153, 154 
Mirrors, plane, laws of the reflec- 
tion of light by, 54 



212 



N 



OBLE'S method of calcula- 
tion, 147-153 



PACING and pedometer, 43-45 
Parabola, to find the area of 
a, 105 

to find the area of a seg- 
ment of a, 105 
Parallelogram, to find the area of 

a, 83-85 
Parallels, standard, 205 

establishment of, 
196 
Pedometer and pacing, 43-45 
Pedometers, wheel, 143 
Perch, 42 

Perpendicular, to erect a, at a 
point in a straight 
line, 49 
to erect a, with the as- 
sistance of the angle- 
mirror, 59, 60 
to let fall a, to a straight 
line from a point, 49, 
50 
to let fall a, with the as- 
sistance of the angle- 
mirror, 60-62 
Pins, marking 32, 41, 42 

plumbing the, and levelling 

the chain, 198, 199 
tally, 197 

wooden, for marking, 21 
Point, indication of a, in the field, 
20 

marking a, 20 
to determine a, in a straight 
line, when it is impossible 
to take position in its pro- 
longation, 25-27 
to find a, in a straight line, 
23-25 



Point, to find a, in the prolongation 

of a straight line, 21-23 
Points, definition of the, to be de- 
termined in surveying, 18 
Pole, 42 

chains and links, reduction 
of, 81, 82 
Poles for marking, 21 
Polygon, survey of a, 77-79 
Pond or forest, to find the length, 
when the straight line 
passes through a, 34-36 
Principal meridian, 205 
Prism for right angles, and its 

use, 65, 6G 
Problems, 81-106 
Public lands of the United States, 
systems of rectangular survey- 
ing for surveying the, 194-208 



UARTER section boundaries, 
202 







RAILROAD, to inflect in curves 
on, 168-179 
Random or trial lines, 200 
Range, constitution of a, 194 
Rectangular surveying, systems 
of, for surveying 
the public lands 
of the United 
States, 194-208 
Reflection, angle of, 55 
Right angles, examples of the ap- 
plication of setting- 
out, 69-75 
instruments for setting- 
out, 46-75 
prism for, and its use, 

65, 66 
to set out with the tape 
measure, 67-69 



213 



River, to find the distance when 
the straight line continues 
across a, 36, 37 
Road, to find the cuttings and 
fillings of a, 167, 168 
to lay out a, on a regular 
grade up a hill, 166-168 
Roads, to inflect in curves on, 

168-179 
Rod, square, 42 
Rods, measuring, and their use, 

28-30 
Rood, 42 

SECTION boundaries, 202 
Sections, 194 
Sections, content of, 195, 196 
Sight trees or line trees, 199 
Signals, 24, 25 
Solar compass, Burt's improved, 

196. 
Square, to find the content of a, 

82, 83 
Stakes, 31 

Standard parallels, 205 
Stones, boundary, 20 
Surface, plane, determination of 

a, 18 
Survey, extent of a, 17 
map of a. 18, 19 
of a polygon, 77-79 
of a three-sided field, 76,77 
of smaller tracts, 76-80 
plotting the notes of a, 155, 

156 
public, the lines of the, 

204, 205 
to determine the angle 
made by two stations oi 
a, 136-143 
to, with the compass 
through any mine, 153, 
154 



Surveying, definition of the points 
to be determined in, 18 

object of, 17 

rectangular, systems of, for 
surveying the public 
lands of the United 
States, 194-208 

trigonometrical, 107-191 
Surveyor's angle-mirror, its con- 
struction and mode ' of 
operation, 53-58 

chain, ordinary, 40 

cross or cross staff, and its 
use, 46-51 
Surveys, rules for altering the 
legs of stations in the 
correcting of, 124-126 

tables of, 192, 193 



TABLE of errors in links and 
decimals, 124 
Tables of latitude and departure, 
180-191 
of surveys, 192, 193 
Tally pins, 197 

Tape measure, measuring with 
the, 31-33 
the, and its appurten- 
ances, 30, 31 
to set out right angles 
with the, G7-69 
Township boundaries, corners for, 
201 
lines, exterior of, 206-208 
measurement of, 197 
Towns, lotting or laying out of, 

156, 157 
Townships, 194 

Tracts, smaller, survey of, 76-80 
Trapezium, to find the area of a, 
101-105 
to find the content of a, 86 



214 



Trapezoid, rule to find the area 

of a, 99 
Trees, sight or line, 199 
Trial or random lines, 200 
Triangle, rules for finding the 
content of a, 8'7-99 
the, considered as spherical, 

113-115 
to determine the area of a. 
109-113 
Triangulation, 107-109 
Trigonometrical surveying, 107- 
191 



UNITED STATES, systems of 
rectangular surveying for 
surveying the public lands of 
the, 194-208 



V 



ARA, chains, 41 

Variation, mean diurnal for 
every month in the year, 153 



TTTHEEL pedometers, 43 



0-A.T-A.ILiOC3-TJE 

OF 

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AMATEUR MECHANICS' WORKSHOP: 

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ARLOT.— A Complete Guide for Coach Painters : 

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BAIRD.— Miscellaneous Papers on Economic Questions. 
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BOOTH. — Marble Worker's Manual : 

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BOOTH and MORFIT.— The Encyclopaedia of Chemistry, 
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BRANNT. — A Practical Treatise on the Manufacture of Soap 
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BRANNT.— A Practical Treatise on the Raw Materials and the 
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BUCKMASTER.— The Elements of Mechanical Physics : 
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BURGH. — Practical Rules for the Proportions of Modern 
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BYLES. — Sophisms of Free Trade and Popular Political 

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BOWMAN.— The Structure of the Wool Fibre in its Relation 
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BYRNE. — Hand-Book for the Artisan, Mechanic, and Engi- 
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The Unity of Law : As Exhibited in the Relations of Physical, 
Social, Mental and Moral Science {1872). Svo. . . $3.S<^ 

CLARK. — Tramv/ays, their Construction and Working: 

Embracing a Comprehensive History of the System. With an ex' 
haustive analysis of the various modes of traction, including horse- 
power, steam, heated water and compressed air; a description of the 
varieties of Rolling stock, and ample details of cost and working ex- 
penses. By D. KiNNEAR Clark. Illustrated by over 200 wood 
engravings, and thirteen folding plates. 2 vols. Svo. . ^12.50 

COLBURN.— The Locomotive Engine : 

Including a Description of its Structure, Rules for Estimating its 
Capabilities, and Practical Observations on its Construction and Man- 
agement. By Zerah Colburn. Illustrated. i2mo. . ^I.oa 

COLLENS.— The Eden of Labor ; or, the Christian Utopia. 
By T. Wharton Collens, author. of " Humanics," "The Historj 
of Charity," etc. l2mo. Paper cover, $1.00; Cloth . $1.2^ 

COOLEY. — A Complete Practical Treatise on Perfumery : 
Being a Hand-book of Perfumes, Cosmetics and other Toilet Articles. 
With a Comprehensiv» Collection of Formulae. By Arnold J. 
COOLEY. i2mo i^i.5& 

COOPER.— A Treatise on the use of Belting for tbe Trans* 
mission of Power. 
With numerous illustrations of approved and actual methods of ar- 
ranging Main Driving and Quarter Twist Belts, and of Belt Fasten 
ings. Examples and Rules in great number for exhibiting and cal- 
culating the size and driving power of Belts. Plain, Particular and 
Practical Directions for the Treatment, Care and Management o'' 
Belts. Descriptions of many varieties of Beltings, together witn 
chapters on the Transmission of Power by Ropes; by Iron and 
Wood Frictional Gearing; on the Strength of Belting Leather; and 
on the Experimental Investigations of Morin, Briggs, and others. Bf 
John H. Cooper, M. E. Svo $3-S^ 

CRAIK.— The Practical American Millwright and Miller. 

By David Craik, Millwright. Illustrated by numerous wood en- 
gravings and two folding plates. Svo $$,os 



HENRY CAREY BAIRD & CO.'S CATALOGUE. 



CREW. — A Practical Treatise on Petroleum : 

Comprising its Origin, Geology, Geographical Distribution, History, 
Chemistry, Mining, Technology, Uses and Transportation. Together 
with a Description of Gas Wells, the Application of Gas as Fuel, etc. 
By Benjamin J. Crew. With an Appendix on the Product and 
Exhaustion of the Oil Regions, and the Geology of Natural Gas in 
Pennsylvania and New York. By Charles A. Ashburner, M. S., 
Geologist in Charge Pennsylvania Survey, Philadelphia. Illustrated 
by 70 engravings. 8vo. 508 pages . . . . ^i^.oo 

CROSS.— The Cotton Yarn Spinner: 

Showing how the Preparation should be arranged for Different 
Counts of Yarns by a System more uniform than has hitherto been 
practiced; by having a Standard Schedule from which we make all 
our Changes. By Richard Cross. 122 pp. i2mo. . 75 

CRISTIANI. — A Technical Treatise on Soap and Candles : 
With a Glance at the Industry of Fats and Oils. By R. S. Cris- 
TIANI, Chemist. Author of " Perfumery and Kindred Arts." Illus- 
trated by 176 engravings. 581 pages, 8vo. . . . ^15.00 

CKISTIANI.— Perfumery and Kindred Arts: 
A Comprehensive Treatise on Perfumery, containing a History of 
Perfumes from the remotest ages to the present time. A complete 
detailed description of the various Materials and Apparatus used in 
the Perfumer's Art, with thorough Practical Instruction and careful 
Formulae, and advice for the fabrication of all known preparations of 
the day, including Essences, Tinctures, Extracts, Spirits, Waters, 
Vinegars, Pomades, Powders, Paints, Oils, Emulsions, Cosmetics, 
Infusions, Pastilles, Tooth Powders and Washes, Cachous, Hair Dyes, 
Sachets, Essential Oils, Flavoring Extracts, etc. ; and full details for 
making and manipulating Fancy Toilet Soaps, Shaving Creams, etc., 
by new and improved methods. With an Appendix giving hints and 
advice for making and fermenting Domestic Wines, Cordials, Liquors, 
Candies, Jellies, Syrups, Colors, etc., and for Perfuming and Flavor- 
ing Segars, Snuff and Tobacco, and Miscellaneous Receipts foi 
various useful Analogous Articles. By R. S. Cristiani, Con- 
sulting Chemist and Perfumer, Philadelphia. 8vo. . . ^10.00 

DAVIDSON.— A Practical Manual of House Painting, Grain- 
ing, Marbling, and Sign- Writing : 
Containing full information on the processes of House Painting in 
Oil and Distemper, the Formation of Letters and Practice of Sign- 
Writing, the Principles of Decorative Art, a Course of Elementary 
Drawing for House Painters, Writers, etc., and a Collection of Useful 
Receipts. With nine colored illustrations of Woods and Marbles, 
and numerous wood engravings. By Ellis A. Davidson. i2mo. 

^3.00 

DAVIES. — A Treatise on Earthy and Other Minerals and 
Mining : 
By D. C. Davies, F. G. S., Mining Engineer, etc. Illustrated by 
76 Eugraviugs, l2mo 15-°*^ 



HENRY CAREY BAIRD & CO.'S CATALOGUE. 



DAVIES. — A Treatise on Metalliferous Minerals and Mining: 
By D. C. Davies, F. G. S.; Mining Engineer, Examiner of MineSr 
Quarries and Collieries. Illustrated by 148 engravings of Geological 
Formations, Mining Operations and Machinery, drawn from thft 
practice of all parts of the world. 2d Edition, i2mo., 450 pages ^5.0d 

DAVIES.— A Treatise on Slate and Slate Quarrying: 

Scientific, Practical and Commercial. By D. C. Davies, F. G. S., 
Mining Engineer, etc. With numerous illustrations and folding 
plate*. i3mo ^2.03 

PAVIS. — A Treatise on Steam-Boiler Incrustation and Meth4 
ods for Preventing Corrosion and the Formation of Scale .' 
By Charles T. Davis. Illustrated by 65 engravings. 8vo. ;?i.5o 

DAVIS.— The Manufacture of Paper: 

Being a Description of the various Processes for the Fabrication, 
Coloring and Finishing of every kind of Paper, Including the Dif- 
ferent Raw Materials and the Methods for Determining their Values, 
the Tools, Machines and Practical Details connected with an intelli- 
gent and a profitable prosecution of the art, with special reference to 
the best American Practice. To which are added a History of Pa- 
per, complete Lists of Paper-Making Materials, List of American 
Machines, Tools and Processes used in treating the Raw Materials, 
and in Making, Coloring and Finishing Paper. By Charles T. 
Davis. Illustrated by 156 engravings. 608 pages, 8vo. ;!>6.oo 

OAVIS.— The Manufacture of Leather: 
Being a description of all of the Processes for the Tanning, Tawing, 
Currying, Finishing and Dyeing of every kind of Leather ; including 
the various Raw Materials and the Methods for Determining their 
Values; the Tools, Machines, and all Details of Importance con- 
nected with an Intelligent an-d Profitable Prosecution of the Art, with 
Special Reference to the Best American Practice. To which are 
added Complete Lists of all American Patents for Materials, Pro- 
cesses, Tools, and Machines for Tanning, Currying, etc. By Charles 
Thomas Davis. Illustrated by 302 engravings and 12 Samples of 
Dyed Leathers. One vol., Svo., 824 pages . . . $10.00 

DAWIDOWSKY— BRANNT.— A Practical Treatise on the 

Raw Materials and Fabrication of Glue, Gelatine, Gelatine 

Veneers and Foils, Isinglass, Cements, Pastes, Mucilages, 

etc. : 

Eased upon Actual Experience. By F. Dawidowsky, Technical 

Chemist. Translated from the German, with extensive additions, 

including a description of the most Recent Ameriean Processes, by 

William T. Brannt, Graduate of the Royal Agricultural College 

of Eldena, Prussia. 35 Engravings. l2mo. . . . |!2.SO 

DE GRAFF. — The Geometrical Stair-Builders' Guide: 

Being a Plain Practical System of Hand-Railing, embracing all it3 
necessary Details, and Geometrically Illustrated by twenty-two Steel 
Engravings; together with the use of the most approved pnnciplei 
til Practical Geometry. By Simon De Graff, Architect. 4X0. 



HENRi CARE\ Eaiki> 6: CO'.S CATALOd'Jxi-. 



DE KONINCK— DIETZ.— A Practical Manual of Chemical 
Analysis and Assaying : 
As applied to the Manufacture of Iron from its Ores, and to Cast Iron, 
Wrought Iron, and Steel, as found in Commerce. By L. L. De 
KoNiNCK, Dr. Sc, and E. Dietz, Engineer. Edited with Notes, by 
Robert Mallet, F. R. S., F. S. G., M. I. C. E., etc. American 
Edition, Edited with Notes and an Appendix on Iron Ores, by A. A. 
Fesquet, Chemist and Engineer. i2mo. . . . ^^2.50 

DUNCAN.— Practical Surveyor's Guide: ^ 

Containing the necessary information to make any person of com- 
mon capacity, a finished land surveyor without the aid of a teacher 
By Andrew Duncan. Illustrated. lamo. . . . ^1.25 

DUPLAIS. — A Treatise on the Manufacture and Distillation 
of Alcoholic Liquors : 
Comprising Accurate and Complete Details in Regard to Alcohol 
from Wine, Molasses, Beets, Grain, Rice, Potatoes, Sorghum, Aspho 
del, Fruits, etc.; with the Distillation and Rectification of Brandy, 
Whiskey, Rum, Gin, Swiss Absinthe, etc., the Preparation of Aro- 
matic Waters, Volatile Oils or Essences, Sugars, Syrups, Aromatic 
Tinctures, Liqueurs, Cordial Wines, Effervescing Wines, etc., the 
Ageing of Brandy and the improvement of Spirits, with Copioaa 
Directions and Tables for Testing and Reducing Spirituous Liquors, 
etc., etc. Translated and Edited from the French of MM. DuPLAis, 
Aine et Jeune. By M. McKennie, M. D. To which are added the 
United States Internal Revenue Regulations for the Assessment and 
Collection of Taxes on Distilled Spirits. Illustrated by fourteen 
folding plates and several wood engravings. 743 pp. 8vo. $10 oa 

aUSSAaCE.— Practical Treatiseon the Fabrication of Matches, 
Gun Cotton, and Fulminating Powder. 
By Professor H. DussAUCE. i2mo $300 

OYER AND COLOR-MAKER'S COMPANION: 

Containing upwards of two hundred Receipts for making Colors, on 
the most approved principles, for all the various styles and fabrics now 
in existence; with the Scouring Process, and plain Directions for 
Preparing, Washing-ofF, and Finishing the Goods. i2mo. ^i 25 

aDWARDS. — A Catechism of the Marine Steam-Engine, 

For the use of Engineers, Firemen, and Mechanics. A Practical 
Work for Practical Men. By Emory Edwards, Mechanical Engi- 
neer. Illustrated by sixty-three Engravings, including examples of 
the most modern Engines. Third edition, thoroughly revised, with 
much additional matter. 12 mo. 414 pages . . . ^2 GO 

CDWARDS. — Modern American Locomotive Engines, 

Their Design, Construction and Management. By Emory EdwaRDS. 
Illustrated i2mo ;^2.oo 

SDWARDS.— The American Steam Engineer: 

Theoretical and Practical, with examples of the latest and most ap- 
proved American practice in the design and construction of Steam 
Engines and Boilers. For the use of engineers, machinists, boiler- 
i)«'\kers, and engineering studenis. By Emory Edwards. Fully 
41usirated, 419 pages. i2mo. .... ;?2.50 



ra HENRY CAREY BAIRD & CO.'S CATALOGUE. 

EDWARDS. — Modern American Marine Engines, Boilers, an4 
Screw Propellers, 
Their Design and Construction. Showing the Present Praaice of 
the most Eminent Engineers and Marine Engine Builders in the 
United States. Illustrated by 30 large and elaborate plates. 4to. ^S.oa 
EDWARDS.— The Practical Steam Engineer's Guide 
In the Design, Construction, and Management of American Stationary, 
Portable, and Steam Fire- Engines, Steam Pumps, Boilers, Injectors, 
Governors, Indicators, Pistons and Rings, Safety Valves and Steam 
Gauges. For the use of Engineers, Firemen, and Steam Users. By 
Emory Edwards. Illustrated by 119 engravings. 420 pages. 

i2mo J? 2 50 

EISSLER.— The Metallurgy of Gold: 

A Practical Treaiise 011 the Metallurgical Treatment of Gold-Bear- 
ing Ores, including the Processes of Concentration and Chlorination, 
and the Assaying, Melting, and Refining of Gold. By M. Eissler. 

"With 132 Illustrations. l2mo $3-SO 

EISSLER.— The Metallurgy of Silver : 

A Practical Treatise on the Amalgamation, Roasting, and Lixiviation 
of Silver Ores, including the Assaying, Melting, and Refining of 
Silver Bullion. By M. Eissler. 124 Illustrations. 336 pp. 

i2mo M-2S 

ELDER, — Conversations on the Principal Subjects of Political 
Economy. 
By Dr. William Elder. 8vo. ... . . . ^2.50 

ELDER.— Questions of the Day, 

Economic and Social. By Dr. William Elder. 8vo. . ^3.00 
ERNL— Mineralogy Simplified. 

Easy Methods of Determining and Classifying Minerals, including 
Ores, by means of the Blowiiipe, and by Humid Chemical Analysis, 
based on Professor von Kobell's Tables for the Determination of 
Minerals, with an Introduction to Modern Chemistry. By Henry 
Erni, A.m., M.D., Professor of Chemistry. Second Edition, rewritten, 
enlarged and improved. i2mo. ..... $3°^ 

FAIRBAIRN.— The Prmciples of Mechanism and Machinery 
of Transmission • 
Comprising the Prmciples of Mechanism, Wheels, and Pulleys, 
Strength and Proportions of Shafts, Coupling of Shafts, and Engag- 
ing and Disengaging Gear. By SiR William Fairbairn, Bart 
C. E. Beautifully illustrated by over 1 50 wood-cuts. In one 
volume. i2mo .....•••• $2.^C 

FLEMING.— Narrow Gauge Railways in America. 

A Sketch of their Rise, Progress, and Success. Valuable Statistics 
as to Grades, Curves, Weight of Rail, Locomotives, Cars, etc. By 

Howard Fleming. Illustrated, 8vo $1 00 

FORSYTH.— Book of Designs for Headstones, Mural, and 
other Monuments : 
Contaming 78 Designs. By James Forsyth. With an Introduction 
"hy Charles Boutell, M. A. 4 to., cloth . . - $5 ^ 



HENRY CAREY BAIRD & CO.'S CATALOGUE. 13 



FRANKEL— HUTTER.— A Practical Treatise on the Manu» 
facture of Starch, Glucose, Starch-Sugar, and Dextrine: 
Based on the German of Ladislaus Von Wagner, Professor in the 
Royal Technical High School, Buda-Pest, Hungary, and other 
authorities. By Julius Frankel, Graduate of the Polytechnic 
School of Hanover. Edited by Robert Hutter, Chemist, Practical 
Manufacturer of Starch-Sugar. Illustrated by 58 engravings, cover- 
ing every branch of the subject, including examples of the most 
Recent and Best American Machinery. 8vo., 344 pp. . ^3.50 

GARDNER.— The Painter's Encyclopaedia: 

Containing Definitions of all Important Words in the Art of Plain 
and Artistic Painting, with Details of Practice in Coach, Carriage, 
Railway Car, House, Sign, and Ornamental Painting, including 
Graining, Marbling, Staining. Varnishing, Polishing, Lettering, 
Stenciling, Gilding, Bronzing, etc. By Franklin B. Gardner. 
158 Illustrations. i2mo. 427 pp ;^2.oa 

GARDNER.— Everybody's Paint Book: 

A Complete Guide to the Art of Outdoor and Indoor Painting, De- 
signed for the Special Use of those who wish to do their own work, 
and consisting of Practical Lessons in Plain Painting, Varnishing, 
Polishing, Staining, Paper Hanging, Kalsomining, etc., as well as 
Directions for Renovating Furniture, and Hints on Artistic Work for 
Home Decoration. 38 Illustrations. i2mo., 183 pp. . ^i.oo 

GEE. — The Goldsmith's Handbook : 

Containing full instructions for the Alloying and Working of Gold, 
including the Art of Alloying, Melting, Reducing, Coloring, Col- 
lecting, and Refining: the Processes of Manipulation, Recovery of 
Waste; Chemical and Physical Properties of Gold; with a New 
System of Mixing its Alloys; Solders, Enamels, and other Useful 
Rules and Recipes. By George E. Gee. i2mo. . . ^1-75 

GEE. — The Silversmith's Handbook : 

Containing full instructions for the Alloying and Working of Silver, 
including the different modes of Refining atld Melting the Metal ; its 
Solders ; the Preparation of Imitation Alloys ; Methods of Manipula- 
tion ; Prevention of Waste ; Instructions for Improving and Finishing 
the Surface of the Work ; together with other Useful Information and 
Memoranda. By George E. Gee. Illustrated. i2mo. ^i-7S 

GOTHIC ALBUM FOR CABINET-MAKERS: 

Designs for Gothic Furniture. Twenty-three plates. Oblong ;^2.oo 

GRANT.— A Handbook on the Teeth of Gears : 

Their Curves, Properties, and Practical Construction, By George 
B. Grant. Illustrated. Third Edition, enlarged. 8vo, ^1.50 

GREENWOOD.— Steel and Iron: 
Comprising the Practice and Theory of the Several Methods Pur- 
sued in their Manufacture, and of their Treatment in the Rolling- 
Mills, the Forge, and the Foundry. By William Henry Green- 
wood, F. C. S. With 97 Diagrams, 536 pages. i2mo. ;SS2.ao 



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GREGORY, — Mathematics for Practical Men : 

Adapted to the Pursuits of Surveyors, Architects, Mechanics, and 
Civil Engineers. By Olinthus Gregory. 8vo., plates $3.00 

GRIMSHAW.— Saws : 

The History, Development, Action, Classification, and Comparison 
of Saws of all kinds. IVM Copious Appendices. Giving the details 
of Manufacture, Filing, Setting, Gumming, etc. Care and Use of 
Saws; Tables of Gauges; Capacities of Saw-Mills; List of Saw- 
Patents, and other valuable information. By Robert Grimshaw. 
Second and greatly enlarged edition, with Supplement, and 354 
Illustrations. Quarto ^S-OO 

GRISWOLD. — Railroad Engineer's Pocket Companion for tha 
Field : 
Comprising Rules for Calculating Deflection Distances and Angles, 
Tangential Distances and Angles, and all Necessary Tables for En- 
gineers; also the Art of Levelling from Preliminary Survey to the 
Construction of Railroads, intended Expressly for the Young En- 
gineer, together with Numerous Valuable Rules and Examples. By 
W. Griswold. i2mo., tucks ^i-75 

GRUNER. — Studies of Blast Furnace Phenomena: 

By M. L; Gruner, President of the General Council of Mines ol 
France, and lately Professor of Metallurgy at the Ecole des Mines. 
Translated, with the author's sanction, with an Appendix, by L. D. 
B. Gordon, F. R. S. E., F. G. S. 8vo. , . . ^^2.50 

Hand-Book of Useful Tables for the Lumberman, Farmer and 
Mechanic: 
Containing Accurate Tables of Logs Reduced to Inch Board Meas* 
ure. Plank, Scantling and Timber Measure; Wages and Rent, by 
Week or Month; Capacity of Granaries, Bins and Cisterns; Land 
Measure, Interest Tables, with Directions for Finding the Interest on 
any sum at 4, 5, 6, 7 and 8 per cent., and many other Useful Tables. 
32 mo., boards. 186 pages .,,... .25 

HASERICK.— The Secrets of the Art of Dyeing Wool, Cotton, 
and Linen, 
Including Bleaching and Coloring Wool and Cotton Hosiery and 
Random Yarns. A Treatise based on Economy and Practice. By 
E. C. Haserick. Illustrated by 323 Dyed Patterns of the Yami 
or Fabrics. 8vo %1-'^Q 

HATS AND FELTING: 

A Practical Treatise on their Manufacture. By a Practical Hatter. 
Illustrated by Drawings of Machinery, etc. 8vo. . . ^1.25 

H OFFER. — A Practical Treatise on Caoutchouc and Gutta 
Percha, 
Comprising the Properties of the Raw Materials, and the manner nl" 
Mixing and Working them ; with the Fabrication of Vulcanized and 
Hard Rubbers, Caoutchouc and Gutta Pescha Compositions, Wate» 
proof Substances, Elastic Titesues, the Utilization of Waste, etc., etc 
From the German of Raimund Hoffer, By W. T. Brannt. 
Illustrated i2mo ^2.50 



HENRY CAREY BAIRD & CO.'S CATALOGUE. 15 

HAUPT— RHAWN.— A Move for Better Roads : 

Essays on Road-making and Maintenance and Road Laws, for 
which Prizes or Honorable Mention were Awarded through the 
University of Pennsylvania by a Committee of Citizens of Philadel- 
phia, with a Synopsis of other Contributions and a Review by the 
Secretary, Lewis M. Haupt, A. M., C. E. ; also an Introduction by 
William H. Rhawn, Chairman of the Committee. 319 pages. 
8vo ^2.00 

HUGHES. — American Miller and Millwright's Assistant: 
By William Carter Hughes. i2mo ^1.50 

HULME. — Worked Examination Questions in Plane Geomet- 
rical Drawing : 
For the Use of Candidates for the Royal Military Academy, Wool- 
wich ; the Royal Military College, Sandhurst ; the Indian Civil En- 
gineering College, Cooper's Hdl ; Indian Public Works and Tele- 
graph Departments ; Royal Marine Li^ht Infantry; the Oxford and 
Cambridge Local Examinations, etc. By F. Edward Hulme, F. L. 
S., F. S. A., Art-Master Marlborough College. Illustrated by 300 
examples. Small quarto .....<. ^2.50 

JERVIS.— Railroad Property: 

A Treatise on the Construction and Management of Railways; 
designed to afford useful knowledge, in the popular style, to tha 
holders of this class of property ; as well as Railway Managers, Offi- 
cers, and Agents. By John B. Jervis, late Civil Engineer of the 
Hudson River Railroad, Croton Aqueduct, etc. i2mo., cloth ^2.0G 

KEENE.— A Hand-Book of Practical Gauging: 

For the Use of Beginners, to which is added a Chapter on Bistilla. 
tion, describing the process in operation at the Custom-House fol 
ascertaining the Strength of Wines. By James B. Keene, gf H. M. 
Customs. 8vo. $f-25 

KELLEY. — Speeches, Addresses, and Letters on Industrial and 
Financial Questions : 
By Hon. William D. Kelley, M. C. 544 pages, 8vo. . $3.00 

SELLOGG.— A New Monetary System : 

The only means of Securing the respective Rights of Labor and 
Property, and of Protesting the Public from Financial Revulsions.' 
By Edward Kellogg. Revised from his work on "Labor and 
' other Capital." With numerous additions from his mpnuscvipt. 
Edited by MARY Kellogg Putnam, Fifth edition. To which i» 
added a Biographical Sketch of the Author. One volume, i2mo. 

Paper cover ^I.oo 

Bound in cloth 1.5a 

KEMLO.— Watch-Repairer's Hand-Book : 

Being a Complete Guide to the Young Beginner, in Taking Apart, 
Putting Together, and Thoroughly Cleaning the English Lever and 
other Foreign Watches, and all American Watches. By F. Kemlo, 
■practical Watchmaker. With Illustrations. i2mo. . $l.2i 



i^ HENRY CARGY BAIRD & CO.'S CATALOGUE. 

KENTISH.— A Treatise on a Box of Instruments, 

And the Slide Rule ; with the Theory of Trigonometry and Log* 
rithms, including Practical Geometry, Surveying, Measuring of Tim. 
ber, Cask and Malt Gauging, Heights, and Distances. By Thomaj 
Kentish. In one volume. i2mo. . . . . Si 2=; 

KERL.— The Assayer's Manual: 

An Abridged Treatise on the Docimastic Examination of Ores, and 
Furnace and other Artificinl Products. By Bruno Kerl, Professor 
in the Royal School of Mines. Translated from the German by 
William T. Brannt. Second American edition, edited with Ex- 
tensive Additions by F. Lynwood Garrison, Member of the 
American Institute of Mining Engineers, etc. Illustrated by 87 en- 
gravings. 8vo. . ^3.00 

KICK.— Flour Manufacture . 

A Treatise on Milling Science and Practice. By Frederick Kick, 
Imperial Regieningsmth, Professor of Mechanical Technology in the 
imperial German Polytechnic Institute, Prague. Translated from 
the second enlarged and revised edition with supplement by H. H. 
P. PowLES, Assoc. Memb. Institution of Civil Engineers. Illustrated 
with 28 Plates, and 167 Wood-cuts, 367 pages. 8vo. , ^10,00 
KINGZETT,— The History, Products, and Processes of the 
Alkali Trade : 
Including the most Recent Improvements. By Charles Thomas 
KiNGZETT, Consulting Chemist. With 23 illustrations. 8vo. ^2.50 
KIRK. — The Founding of Metals : 
A Practical Treatise on the Melting of Iron, with a Description of the 
Founding of Alloys ; also, of all the Metals and Mineral Substances 
used in the Art of Founding. Collected from original sources. By 
Edward Kirk, Practical Foundryman and Chemist. Illustrated, 

Third edition. 8vo. ^2.50 

LANDRIN.— A Treatise on Steel : 
Comprising its Theory, Metallurgy, Properties, Practical Working, 
and Use. By M. H. C. Landrin, Jr., Civil Engineer. Translated 
from the French, with Notes, by A. A. Fesquet, Chemist and En- 
gineer. With an Appendix on the Bessemer and the Martin PrO' 
cesses for Manufacturing Steel, from the Report of Abram S. Hewitt 
United States Commissioner to the Universal Exposition, Paris, 1867J 

I2mo $3-OC 

LANGBEIN.— A Complete Treatise on the Electro-Deposition 
of Metals : 
Translated from the German, with Additions, by Wm. T. Brannt. 
125 illustrations. 8vo ^4.00 

LARDNER.— The Steam-Engine : 

Fer the Use of Beginners. Illustrated. lamo, ... 75 
LEHNER.— The Manufacture of Ink: 

Comprising the Raw Materials, and the Preparation of Writing, 
Copying and Hektograph Inks, Safety Inks, Ink Extracts and Pow- 
ders, etc. Translated from the German of Sigmund Lehner, with 
additions by William T. Brannt. Illustrated. i2mo. ;g2.oo 



\ 



HENRY CAR^\ BAIRD & CO.'S CATALOGUE. 17 

LARKIN. — The Practical Brass and Iron Founder's Guide: 
A Concise Treatise on Brass Founding, Moulding, the Metals and 
their Alloys, etc. ; to which are added Recent Improvements in the 
Manufacture of Iron, Steel by the Bessemer Process, etc., etc. By 
James Larkin, late Conductor of the Brass Foundry Department in 
Reany, Neafie & Co.'s Penn Works, Philadelphia. New edition, 
revised, with extensive additions. i2mo. . . . ^2,50 

IJEROUX.—A Practical Treatise on the Manufacture of 
Worsteds and Carded Yarns : 
Comprising Practical Mechanics, with Rules and Calculations applied 
to Spinning; Sorting, Cleaning, and Scouring Wools; the English 
and French Methods of Combing, Drawing, and Spinning Worsteds, 
and Manufacturing Carded Yarns. Translated from the French of 
Charles Leroux, Mechanical Engineer and Superintendent of a 
Spinning-Mill, by Horatio Paine, M. D., and A, A. Fesquet, 
Chemist and Engineer. Illustrated by twelve large Plates. To which 
is added an Appendix, containing Extracts from the Reports of the 
International Jury, and of the Artisans selected by the Committee 
appointed by the Council of the Society of Arts, London, on Woolen 
and Worsted Machinery and Fabrics, as exhibited in the Paris Uni- 
versal Exposition, 1867. 8vo. . . . ■ . . ^5.00 

LEFFEL. — The Construction of Mill-Dams : 
Comprising also the Building of Race and Reservoir Embankments 
and Head-Gates, the Measurement of Streams, Gauging of Water 
Supply, etc. By James Leffel & Co. Illustrated by 58 engravings. 
8vo. ^2.50 

LESLIE.— Complete Cookery: 

Directions for Cookery in its Various Branches. By Miss Leslie. 
Sixtieth thousand. Thoroughly revised, with the addition of New 
Receipts. i2mo IS1.50 

LE VAN. — The Steam Engine and the Indicator : 

Their Origin and Progressive Development; including the Most 
Recent Examples of Steam and Gas Motors, together with the Indi- 
cator, its Principles, its Utility, and its Application. By William 
Barnet Le Van. Illustrated by 305 Engravings, chiefly of Indi- 
cator-Cards. 469 pp. Svo. ...... ^.00 

tlEBER.— Assayer's Guide ; 
Or, Practical Directions to Assayers, Miners, and Smelters, for the 
Tests and Assays, by Heat and by Wet Processes, for the Ores of all 
the principal Metals, of Gold and Silver Coins and Alloys, and of 
Coal, etc. By Oscar M. Lieber. i2mo, . . . ^1.25 

Lockwood's Dictionary of Terms : 

Used in the Practice of Mechanical Engineering, embracing those 
Current in the Drawing Office, Pattern Shop, Foundry, Fitting, Turn- 
ing, Smith's and Boiler Shops, etc., etc., comprising upwards of Six 
Thousand Definitions. Edited by a Foreman Pattern Maker, author 
of " Pattern Making." 417 pp. l2mo. . . . i^J.oo 



i8 HENRY CAREY BAIRD & CO.'S CATALOGUE. 

' ' ' — — '■— - - ^ 

trUKIN.— Amongst Machines; 

Embracing Descriptions of the various Mechanical Appliances used 
in the Manufacture of Wood, Metal, and other Substances. J2mo. 

iUKIN.— The Boy Engineers : 
What They Did, and How They Did It. With 30 plates. tSmo. 

LUKIN.— The Young Mechanic : ^'^^ 

P*ractical Carpentiy. Containing Directions for the Use of all kinds 
j>i Tools, and for Construction of Steam-Engines and Mechanical 
Models, including the Art of Turning in Wood and Metal. By John 
LUKiN, Author of "The Lathe and Its Uses," etc. Illustrated. 
i2mo $i-7S 

MAIN and BROWN.— Questions on Subjects Connected with 

the Marine Steam-Engine : 

And Examination Papers; with Hints for their Solution. By 

Thomas J. Main, Professor of Mathematics, Royal ^aval College, 

and Thomas Brown, Chief Engineer, R. N. i2mo., cloth . li-SGi 

MAIN and BROWN. — The Indicator and Dynamometer: 
With their Practical Applications to the Steam-Engine. By Thomas 
J. Main, M. A. F. R., Ass't S. Professor Royal Naval College, 
Portsmouth, and Thomas Brown, Assoc. Inst. C. E., Chief Engineer 
R. N., attached to the R. N. College. Illustrated. 8vo. . ^1.50 

MAIN and BROWN.— The Marine Steam-Engine. 

By Thomas J. Main, F. R. Ass't S. Mathematical Professor at the 
Royal Naval College, Portsmouth, and Thomas Brown, Assoc. 
Inst. C. E., Chief Engineer R. N. Attached to the Royal NavaJ 
College. With numerous illustrations. 8vo. . . ^5.00 

MAKINS.— A Manual of Metallurgy: 

By George Hogarth Makins. 100 engravings. Second edition 
rewritten and much enlarged. i2mo., 592 pages . , fo-oo 

MARTIN.— Screw-Cutting Tables, for the Use of Mechanical 

Engineers : 
Showing the Proper Arrangement of Wheels for Cutting the Threads 
of Screws of any Required Pitch; with a Table for Making the Uni- 
versal Gas-Pipe Thread and Taps. By W. A. Martin, Engineer. 
8vo 50 

MICHELL.— Mine Drainage: 

Being a Complete and Practical Treatise on Direct-Acting Under* 
jTTound Steam Pumping Machinery. With a Description of a larg* 
number of the best known Engines, their General Utility and tha 
Special Sphere of their Action, the Mode of their Application, and 
their Merits compared with other Pumping Machinery. By Stephen 
Michell. Illustrated by 137 engraving*. 8vo., 277 pages . $6.00 

MOLESWORTH.— Pocket-Book of Useful Formulae and 

Memoranda for Civil and Mechanical Engineers. 

By Guilford L. Molesworth, Member of the Institution of Civil 

Engineers, Chief Resident Engineer of the Ceylon Railway. Full. 

bound in Pocket-book form . . . • • • jtl.oo 



HENRY CAREY BAIRD & C0.'» CATALOGUE. 19 

MOORE. — The Universal Assistant and the Complete Me- 
chanic : 

Containing over one million Industrial Facts, Calculations, Receipt!, 
Processes, Trades Secrets, Rules, Business Forms, Legal Items, Etc., 
in every occupation, from the Household to the Manufactory. Bf 
R. Moore. Illustrated by 500 Engravings. lamo. . ^^2.50 

MORRIS.— Easy Rules for the Measurement of Earthwrorks : 
By means of the Prismoidal Formula. Illustrated with Numerous 

, Wood-Cuts, Problems, and Examples, and concluded by an Exten. 
sive Table for finding the Solidity in cubic yards from Mean Areas. 
The whole being adapted for convenient use by Engineers, Surveyors,. 
Contractors, and others needing Correct Measurements of Earthwork. 
By Elwood Morris, C. E. 8vo $1.50 

MORTON. — The System of Calculating Diameter, Circumfer- 
ence, Area, and Squaring the Circle : 
Together with Interest and Miscellaneous Tables, and other informa- 
tion. By James Morton. Second Edition, enlarged, with the 
Metric System. i2mo. ....... 50 

NAPIER.— Manual of Electro-Metallurgy: 

Including the Application of the Art to Manufacturing Processes. 
By James Napier. Fourth American, from the Fourth London 
edition, revised and enlarged. Illustrated by engravings. 8vo. 

NAPIER. — A System of Chemistry Applied to Dyeing. 

By James Napier, F. C. S. A New and Thoroughly Revised Edi- 
tion. Completely brought up to the present state of the Science, 
including the Chemistry of Coal Tar Colors, by A. A. Fesquet, 
Chemist and Engineer. With an Appendix on Dyeing and Calico 
Printing, as shown at the Universal Exposition, Paris, 1867. Illus- 
trated. 8vo. 422 pages . . . . . . . $3.50 

NEVILLE.— Hydraulic Tables, Coefficients, and Formulae, for 
finding the Discharge of Water from Oriiices, Notches, 
Weirs, Pipes, and Rivers : 
Third Edition, with Additions, consisting of New Formulae for the 
Discharge from Tidal and Flood Sluices and Siphons ; general infor- 
mation on Rainfall, Catchment-Basins, Drainage, Sewerage, Wate* 
Supply for Towns and Mill Power. By Tohn Neville, C. E. M. R. 
I. A. ; Fellow of the Royal Geological Society of Ireland. Thick 
l2mo i^S'SO 

NEWBERY.— Gleanings from Ornamental Art of every 
style ; 
Drawn from Examples in the British, South Kensington, Indian, 
Crystal Palace, and other Museums, the Exhibitions of 1851 and 
1862, and the best English and Foreign works. In a series of 100 
exquisitely drawn Plates, containing many hundred examples. By 
Robert Newbery. 4to. :^ 12.50 

NICHOLLS. —The Theoretical and Practical Boiler-Maker and 
Engineer's Reference Book: 
Containing a variety of Useful Information for Employers of Labor. 
Fwemen and Working Boiler-Makers, Iron, Copper, and Tinsmith* 



XO HENRY CAREY BAIRD & CO.'S CATALOGUE. 

Draughtsmen, Engineers, the General Steam-using Public, and for tha 
Use of Science Schools and Classes. By Samuel Nicholls. Illus* 
trated by sixteen plaies, i2mo. ..... $2.50 

NICHOLSON.— A Manual of the Art of Bookbinding : 

Containing full instructions in the different Branches of Forwarding, 
Gilding, and Finishing. Also, the Art of Marbling Book-edges and 
Paper. By James B. Nicholson. Illustrated. i2mo., cloth $2.25 

NICOLLS.— The Railway Builder: 

A Hand-Book for Estimating the Probable Cost of American Rail* 
way Construction and Equipment. By William J. NiGOLLS, Civii 
Engineer. Illustrated, full bound, pocket-book form . ;g2.oo 

NORMANDY.— The Commercial Handbook of Chemical An- 
alysis : 
Or Practical Instructions for the Determination of the Intrinsic of 
Commercial Value of Substances used in Manufactures, in Trades, 
and in the Arts. By A. Normandy. New Edition, Enlarged, and 
to a great extent rewritten. By Henry M. Noad, Ph.D., F.R.S., 
thick i2mo j^S-OO 

MORRIS. — A Handbook for Locomotive Engineers and Ma. 
chinists : 
Comprising the Proportions and Calculations for Constructing Loco- 
motives; Manner of Setting Valves; Tables of Squares, Cubes, Areas, 
etc., etc. By Septimus Norris, M. E. New edition. Illustrated, 
12010 ^1.50 

HYSTROM. — A New Treatise on Elements of Mechanics : 
Establishing Strict Precision in the Meaning of Dynamical Terms : 
accompanied with an Appendix on Duodenal Arithmetic and Me- 
trology. By John W. Nystrom, C. E. Illustrated. 8vo. $2.00 

KYSTROM. — On Technological Education and the Construc- 
tion of Ships and Screw Propellers : 
For Naval and Marine Engineers. By John W. Nystrom, lata 
Acting Chief Engineer, U. S. N. Second edition, revised, with addi- 
tional matter. Illustrated by seven engravings. i2mo. . 1^1.50 

O'NEILL. — A Dictionary of Dyeing and Calico Printing: 
Containing a brief account of all the Substances and Processes in 
use in the Art of Dyeing and Printing Textile Fabrics ; with Practical 
Receipts and Scientific Information. By Charles O'Neill, Analy- 
tical Chemist. To which is added an Essay on Coal Tar Colors and 
their application to Dyeing and Cahco Printing. By A. A. Fesquet, 
Chemist and Engineer. With an appendix on Dyeing and Calico 
Printing, as shown at the Universal Exposition, Paris, 1867. 8vo., 
491 pages JJ53-50 

pRTON. — Underground Treasures-. 

How and Where to Find Them. A Key for the Ready Determination 
of all the Useful Minerals within the United States. By James 
Orton, A.m., Late Professor of Natural History in Vassar College, 
N. Y.; Cor. Mem. of the Academy of Natural Sciences, Philadelphia, 
and of the Lyceum of Natural History, New York ; author of the 
•'Andes and the Amazon." etc. A New Edition, with Additions. 
Illustrated , $i.S9 



HENRY CAREY BAIRD & CO.'S CATALOGUE. 21 



OSBORN. — The Prospector's Field Book and Guide : 

In the Search for and the Easy Determination of Ores and Other 
Useful Minerals. By Prof. H. S. OsBORN, LL. D., Author of 
*' The Metallurgy of Iron and Steel ; " "A Practical Manual of 
Minerals, Mines, and Mining." Illustrated by 44 Engravings. 
l2mo . $1.50 

OSBORN". — A Practical Manual of Minerals, Mines and Min- 
ing: 
Comprising the Physical Properties, Geologic Positions, Local Occur- 
rence and Associations of the Useful Minerals; their Methods of 
Cliemical Analysis and Assay : together with Various Systems of 
Excavating and Timbering, Brick and Masonry Work, during Driv- 
ing, Lining, Bracing and other Operations, etc. By Prof. H. S. 
OsBORN, LL. D., Author of the " Metallurgy of Iron and Steel." 
Illustrated by 171 engravings from original drawings. 8vo. $4-$^ 

OVERMAN.— Th«i Manufacture of Steel: 

Containing the Practice and Principles of Working and Making Steel. 
A Handbook for Blacksmiths and Workers in Steel and Iron, Wagon 
Makers, Die Sinkers, Cutlers, and Manufacturers of Files and Hard- 
ware, of Steel and Iron, and for Men of Science and Art. By 
Frederick Overman, Mining Engineer, Author of the " Manu- 
facture of Iron," etc. A new, enlarged, and revised Edition. By 
A. A. Fesquet, Chemist and Engineer. l2mo. . , ^1.50 

OVERMAN.— The Moulder's and Founder's Pocket Guide : 
A Treatise oiu Moulding and Founding in Green-sand, Dry-sand, Loam, 
and Cement; the Moulding of Machine Frames, Mill-gear, Hollow- 
ware, Ornaments, Trinkets, Bells, and Statues ; Description of Moulds 
for Iron, Bronze, Brass, and other Metals ; Plaster of Paris, Sulphur, 
Wax, etc. ; the Construction of Melting Furnaces, the Melting and 
Founding of Metals ; the Composition of Alloys and their Nature, 
etc., etc. By Frederick Overman, M. E. A new Edition, to 
which is added a Supplement on Statuary and Ornamental Moulding, 
Ordnance, Malleable Iron Castings, etc. By A. A. Fesquet, Chem- 
ist and Engineer. Illustrated by 44 engravings. l2mo. . ;^2.00, 

PAINTER, GILDER, AND VARNISHER'S COMPANION;f 
Containing Rules and Regulations in everything relating to the ArtS 
of Painting, Gilding, Varnishing, Glass-Staining, Graining, Marbling 
Sign- Writing, Gilding on Glass, and Coach Painting and Varnishing; 
Tests for the Detection of Adulterations in Oils, Colors, etc. ; and a 
Statement of the Diseases to which Painters are peculiarly liable, with 
the Simplest and Best Remedies. Sixteenth Edition. Revised, with 
an Appendix. Containing Colors and Coloring — Theoretical and 
Practical. Comprising descriptions of a great variety of Additional 
Pigments, their Qualities and Uses, to which are added. Dryers, and 
Modes and Operations of Painting, etc. Together with Chevreul's 
Principles of Harmony and Contrast of Colors. l2mo. Cloth ;^l.5o 

PALLETT.— The Miller's, Millwright's, and Engineer's Guide. 
By Henry Pallett. Illustrated. i2mo. . . . ^Ja.oa 



22 HENRY CAREY BAIRD & CO.'S CATALOGUE. 

PERCY. — The Manufacture of Russian Sheet-Iron. 

By John Percy, M. D., F. R. S., Lecturer on Metallurgy at the 
Royal School of Mines, and to The Advance Class of Artillery 
Officers at the Royal Artillery Institution, Woolwich ; Author of 
" Metallurgy." "With Illustrations. 8vo., paper . . 50 cts, 

PERKINS.— Gas and Ventilation : 

Practical Treatise on Gas and Ventilation. With Special Relatiotl 
to Illuminating, Heating, and Cooking by Gas. Including Scientific 
Helps to Engineer-students and others. With Illustrated Diagrams, 
By E. E. Perkins. i2mo., cloth ;^i.25 

PERKINS AND STOWE.— A New Guide to the Sheet-iron 
and Boiler Plate Roller : 
Containing a Series of Tables showing the Weight of Slabs and Pile* 
to Produce Boiler Plates, and of the Weight of Piles and the Sizes of 
Bars to produce Sheet-iron; the Thickness of the Bar Gaugs 
in decimals ; the Weight per foot, and the Thickness on the Bar or 
Wire Gauge of the fractional parts of an inch; the Weight per 
sheet, and the Thickness on the Wire Gauge of Sheet-iron of various 
dimensions to weigh 112 lbs. per bundle; and the conversion of 
Short Weight into Long Weight, and Long Weight into Short. 
Estimated and collected by G. H. Perkins and J. G. Stowe. ^2.50 

POWELI CHANCE— HARRIS.— The Principles of Glass 

Making. 
By Harry J. Powell, B. A. Together with Treatises on Crown and 
Sheet Glass; by Henry Chance, M. A. And Plate Glass, by H. 
G. Harris, Asso. M. Inst. C. E. Illustrated i8mo. . ^51.50 

PROCTOR.— A Pocket-Book of Useful Tables and Formulae 
for Marine Engineers : 
By Frank Proctor. Second Edition, Revised and Enlarged. 
Full-bound pocket-book form ....,, ^1.50 

REGNAULT.— Elements of Chemistry: 

By M. V. Regnault. Translated from the French by T. Forrest 
Betton, M. D., atid edited, with Notes, by James C. Booth, Melter 
and Refiner U. S. Mint, and William L. Faber, Metallurgist and 
Mining Engineer. Illustrated by nearly 700 wood-engravings. Com- 
prising nearly 1,500 pages. In two volumes, 8vo., cloth . ^7-50 

RICHARDS.— Aluminium : 

Its History, Occurrence, Properties, Metallurgy and Applications, 
including its Alloys. By Joseph W. Richards, A. C, Chemist and 
Practical Metallurgist, Member of the Deutsche Chemische Gesell- 
schaft. Illustrated i^S.OO 

RIFFAULT, VERGNAUD, and TOUSSAINT.— A Practical 
Treatise on the Manufacture of Colors for Painting : 
Comprising the Origin, Definition, and Classification of Colors; the 
Treatment of the Raw Materials ; the best Formulse and the Newest 
Processes for the Preparation of every description of Pigment, and 
the Necessary Apparatus and Directions for its Use ; Dryers ; the 
Testing, Application, and Qualities of Paints, etc., etc. By MM. 
RlFFAULT, Yergnaud, and ToussAlNT. Revised and Edited by M. 



HENRY CAREY BAIRD & CO.'S CATALOGUE. 



T. Malspeyre. Translated from the French, by A. A. FesqUWJ: 

Chemist and Engmeer. Illustrated by Eighty engravings. In one 
vol.. 8vo., 659 pages ....... $7'5*' 

ROPER. — A Catechism of High-Pressure, or Non-Condensing 
Steam -Engines : 
Including the Modelling, Constructing, and Management of Steam- 
Engines and Steam Boilers. With valuable illustrations. By Ste- 
phen Roper, Engineer. Sixteenth edition, revised and enlarged. 
i8mo., tucks, gilt edge $2.0Q 

itOPER. — Engineer's Handy-Book: 

Containing a full Explanation of the Steam-Engine Indicator, and its 
Use and Advantages to Engineers and Steam Users. With Formulae 
for Estimating the Power of all Classes of Steam-Engines ; also, 
Facts, Figure*, Questions, and Tables for Engineers who wish to 
qualify themselves for the United States Navy, the Revenue Service, 
the Mercantile Marine, or to take charge of the Better Class of Sta- 
tionary Steam-Engines. Sixth edition. i6mo., 690 pages, tucks, 
gilt edge ' . . 1^3.50 

ROPER. — Hand-Book of Land and Marine Engines : 
Including the Modelling, Construction, Running, and Management 
of Lan(^ and Marine Engines and Boilers. With ilJustrations. By 
Stephen Roper, Engineer. Sixth edition. i2mo.,ti\cks, gilt edge. 

ROPER.— Hand-Book of the Locomotive : 

Including the Construction of Engines and Boilers, and the Construc- 
tion, Management, and Running of Locomotives. By Stephen 
Roper. Eleventh edition. i8mo., tucks, gilt edge . $2.^(i 

ROPER.— Hand-Book of Modern Steam Eire-Engines. 

With illustrations. By STEPHEN Roper, Engineer, Fourth edition, 
i2mo., tucks, gilt edge 33-50 

ROPER. — Questions and Answers for Engineers. 

This little book contains all the Questions that Engineers will be 
asked when undergoing an Examination for the purpose of procuring 
Licenses, and they are so plain that any Engineer or Fireman of or- 
dinary intelligence may commit them to memory in a short time. By 
Stephen Roper, Engineer. Third edition . . . ^3.00 

ROPER.— Use and Abuse of the Steam Boiler. 
By Stephen Roper, Engineer. Eighth edition, with illustrations. 
l8mo., tucks, gilt edge ^2.00 

ROSE.— The Complete Practical Machinist : 

Embracing Lathe Work, Vise Work, Drills and Drilling, Taps arid 
Dies, Hardening and Tempering, the Making and Use of Tools^ 
Tool Grinding, Marking out Work, etc. By JosHUA Rose. Illus.* 
trated by 356 engravings. Thirteenth edition, thoroughly revised' 
and in great part rewritten. In one vol., i2mo., 439 pages ^2.50; 

ROSE.- Mechanical Drawing Self- Taught: 
Comprising Instructions in the Selection and Preparation of Drawing 
Instruments. Elementary Instruction in Practical Mechanical Draw- 



84 HENRY CAREY BAIRD & CO.'S CATALOGUE. 

ing, together with Examples in Simple Geometry and Elementary 
Mechanism, including Screw Threads, Gear Wheels, Mechanical 
Motions, Engines and Boilers. By Joshua Rose, M. E. Illustrated 
by 330 engravings. 8vo., 313 pages . , . . ^^4.00 

ROSE.— The Slide- Valve Practically Explained: 

Embracing simple and complete Practical Demonstrations of th^ 
operation of each element in a Slide-valve Movement, and illustrat- 
ing the effects of Variations in their Proportions by examples care^ 
fully selected from the most recent and successful practice. By 
Joshua Rose, M. E. Illustrated by 35 engravings . ^i.oo 

ROSS. — The Blowpipe in Chemistry, Mineralogy and Geology: 
Containing all Known Methods of Anhydrous Analysis, many Work- 
ing Examples, and Instructions for Making Apparatus. By Lieut.- 
COLONEL W. A. Ross, R. A., F. G. S. With 120 Illustrations. 
i2mo. .......... ^2,00 

SHAW.— Civil Architecture : 

Being a Complete Theoretical and Practical System of Building, con- 
taining the P'undamental Principles of the Art. By EDWARD Shaw, 
Architect. To which is added a Treatise on Gothic Architecture, etc. 
By Thomas W. Silloway and George M. Harding, Architects. 
The whole illustrated by 102 quarto plates finely engraved on copper. 
Eleventh edition. 4to. ....... $10.00 

SHUNK. — A Practical Treatise on Railway Curves and Loca- 
tion, for Young Engineers. 
By W. F. Shunk, C. E. i2nio. Full bound pocket-book form ;^2.00 

SLATER.— The Manual of Colors and Dye Wares. 

By J. W. Slater. i2mo ;^3.oo 

SLOAN. — American Houses : 

A variety of Original Designs for Rural Buildings. Illustrated by 
26 colored engravings, with descriptive references. By Samuel 
Sloan, Architect. 8vo. $i-SO 

SLOAN. — Homestead Architecture : 

Containing Forty Designs for Villas, Cottages, and Farm-houses, with 
Essays on Style, Construction, Landscape Gardening, Furniture, etc., 
etc. Illustrated by upwards of 200 engravings. By Samuel Sloan, 
Archuect. 8vo $3-50 

SLOANE.— Home Experiments in Science. 

By T. O'CoNOR Sloane, E. M., A. M., Ph. D. Illustrated by 91 
engravings. i2mo. ....... ^1.50 

SMEATON.— Builder's Pocket-Companion : 

Containing the Elements of Building, Surveying, and Architecture; 
with Practical Rules and Instructions connected with the subject. 
By A. C. Smeaton, Civil Engineer, etc. i2mo. . . |i.So 

SMITH.— A Manual of Political Economy. 

By E. Peshine Smith. A New Edition, to which is added a full 
Index. i2mo j!l 25 



HENRY CAREY BAIRD & CO.'S CATALOGUE. 2^ 

SMITH.— Parks and Pleasure - Grounds : 

Or Practical Notes on Country Residences, Villas, Public Parks, and 
Gardens. By Charles H. J. Smith, Landscape Gardener and 
Garden Architect, etc., etc. l2mo. .... ;j2.oo 

SMITH.— The Dyer's Instructor: 

Comprising Practical Instructions in the Art of Dyeing Silk, Cotton, 
Wool, and Worsted, and Woolen Goods ; containing nearly 800 
Receipts. To which is added a Treatise on the Art of Padding; anci 
the Printing of Silk Warps, Skeins, and Handkerchiefs, and the 
various Mordants and Colors for the different styles of such work. 
By David Smith, Pattern Dyer. i2mo. . . . ^2.00 

SMYTH. — A Rudimentary Treatise on Coal and Coal-Mining. 
By Warrington W. Smyth, M. A., F. R. G., President R. G. S. 
of Cornwall. Fifth edition, revised and corrected. With numer- 
ous illustrations. l2mo. ...... ^I-7S 

SNIVELY.— Tables for Systematic Qualitative Chemical AnaU 
ysis. 
By John H. Snively, Phr. D. 8vo. .... $1.00 

SNIVELY. — The Elements of Systematic Qualitative Chemical 
Analysis : 
A Hand-book for Beginners. By John H. Snively, Phr. D. i6mo. 

$2.00 

STOKES.— The Cabinet-Maker and Upholsterer's Companion : 
Comprising the Art of Drawing, as applicable to Cabinet Work; 
Veneering, Inlaying, and Buhl- Work; the Art of Dyeing and Stain- 
ing Wood, Ivory, Bone, Tortoise-Shell, etc. Directions for Lacker- 
ing, Japanning, and Virnishing; to make French Polish, Glues, 
Cements, and ComposiLi'" ns ; with numerous Receipts, useful to work 
men generally. Bv Stokes. Illustrated. A New Edition, with 
an Appendix upor /ench Polishing, Staining, Imitating, Varnishing, 
etc., etc. l2mo i^i-af 

STRENGTH AND OTHER PROPERTIES OF METALS; 
Reports of Experiments on the Strength and other Properties of 
Metals for Cannon. With a Description of the Machines for Testing 
Metals, and of the Classification of Cannon in service. By Officers 
of the Ordnance Department, U. S. Army. By authority of the Secre. 
taryofWar. Illustrated by 25 large steel plates. Quarto . ^lo.oQ 

SULLIVAN.— Protection to Native Industry. 

By Sir Edward Sullivan, Baronet, author of " Ten Chapters on 
Social Reforms." 8vo ^1.50 

SULZ.— A Treatise on Beverages : 

Or the Complete Practical Bottler. Full instructions for Laboratory 
Work, with Original Practical Recipes for all kinds of Carbonated 
Drinks, Mineral Waters, Flavorings, Extracts, Syrups, etc. By 
Chas. Herman Sulz, Technical ChemLst and Practical Bottler, 
IllustTated by 428 Engravings. 818 pp. iivo. . . ^10.00 



HENRY CAREY BAIRt? & CO.'S CATALOGUE. 



SYME. — Outlines of an Industrial Science. 
By David Syme. i2mo. . . ... ;j!2.o« 

TABLES SHOWING THE WEIGHT OF ROUND, 
SQUARE, AND FLAT BAR IRON, STEEL, ETC., 
By Measurement. Cloth ...... 63 

TAYLOR.— Statistics of Coal : 
Including Mineral Bituminous Substances employed in Arts and 
Manufactures; with their Geographical, Geological, and Commercial 
Distribution and Amount of Production and Consumption on the 
American Continent. With Incidental Statistics of the Iron Manu- 
facture. By R. C. Taylor. Second edition, revised by S. S. Halde- 
MAN. Illustrated by five Maps and many wood engravings. 8vo., 
cloth ^10.00 

TEMPLETON.— The Practical Examinator on Steam and th«9 
Steam -Engine: 
With Instructive References relative thereto, arranged for the Use of 
Engineers, Students, and others. By William Templeton, En- 
gineer. i2mo. ^1.25 

THAUSING.— The Theory and Practice of the Preparation of 
Malt and the Fabrication of Beer: 
With especial reference to the Vienna Process of Brewing. Elab- 
orated from personal experience by JuLlus E. Thausing, Professor 
at the School for Brewers, and at the Agricultural Institute, Modling, 
near Vienna. Translated from the German by WiLLlAM T. Brannt, 
Thoroughly and elaborately edited, with much American matter, and 
according to the latest and most Scientific Practice, by A. ScHWARZ 
and Dr. A. H. Bauer. Illustrated by 140 Engravings. 8vo., 815 
pages ;jSl0.oo 

THOMAS.— The Modern Practice of Photography: 

By R. W. Thomas, F. C. S. Svo. .... 75 

THOMPSON.— Political Economy. With Especial Reference 
to the Industrial History of Nations : 
By Robert E. Thompson, M. A., Professor of Social Science in the 
University of Pennsylvania. l2mo. .... #1.50 

THOMSON.— Freight Charges Calculator: 
By Andrew Thomson, Freight Agent. 2iimo. . . ;^i.25 

TURNER'S (THE) COMPANION: 

Containing Instructions in Concentric, Elliptic, and Eccentric Turn. 
hig; also various Plates of Chucks, Tools, and Instruments; and 
Directions for using the Eccentric Cutter, Drill, Vertical Cutter, and 
Circular Rest; with Patterns and Instructions for working them, 
l2mo $i-2S 

TURNING : Specimens of Fancy Turning Executed on the 

Hand or Foot- Lathe: ( 

With Geometric, Oval, and Eccentric Chucks, and Elliptical Cutting 

Frame. By an Amateur. Illustrated by 30 exquisite Photographs. 

4to , . $3.00 



HENRY CAREY BAIRB & CO.'S CATALOGUE. 27 

VAILE. — Galvanized- Iron Cornice-Worker's Manual : 

Containing Instructions in Laying out the Different Mitres, and 
Making Patterns for all kinds of Plain and Circular Work. Also, 
Tables of Weights, Areas and Circumferences of Circles, and other 
Matter calculated to Benefit the Trade. By Charles A. Vaile. 
Illustrated by twenty-one plates. 4to ' I5.00 

VILLE. — On Artificial Manures : 

Their Chemical Selection and Scientific Application to Agriculture. 
A series of Lectures given at the Experimental Farm at Vincennes, 
during 1867 and 1874-75. By M. Georges Ville. Translated and 
Edited by William Crookes, F. R. S. Illustrated by thirty-one 
engravings. 8vo., 450 pages ;^6.oo 

VILLE. — The School of Chemical Manures : 

Or, Elementary Principles in the Use of Fertilizing Agents. From 
the French of M. Geo. Ville, by A. A. Fesquet, Chemist and En- 
gineer. With Illustrations. i2mo. .... $1.25' 

VOGDES. — The Architect's and Builder's Pocket-Companioa 
and Price-Book : 
Consisting of a Shoit but Comprehensive Epitome of Decimals, Duo- 
decimals, Geometry and Mensuration ; vs^ith Tables of United States 
Measures, Sizes, Weights, Strengths, etc., of Iron, Wood, Stone, 
Brick, Cement and Concretes, Quantities of Materials in given Sizes 
and Dimensions of Wood, Brick and Stone; and full and complete 
Bills of Prices for Carpenter's Work and Painting ; also. Rules for 
Computing and Valuing Brick and Brick Work, Stone Work, Paint- 
ing, Plastering, vfiih a Vocabulary of Technical Terms, etc. By 
Frank W. Vogdes, Architect, Indianapolis, Ind. Enlarged, revised, 
and corrected. In one volume, 368 pages, full-bound, pocket-book 

form, gilt edges J2.00 

Cloth . . l.Sa 

VAN CLEVE. — The English and American Mechanic : 

Comprising a Collection of Over Three Thousand Receipts, Rules, 
and Tables, designed for the Use of every Mechanic and Manufac- 
turer. By B. Frank Van Cleve. Illustrated. 500 pp. i2mo. ^2.00 

WAHNSCHAFFE.— A Guide to the Scientific Examination 
of Soils : 

Comprising Select Methods of Mechanical and Chemical Analysis 
and Physical Investigation. Translated from the German of Dr. F. 
WAHNSCHAFFE. With additions by William T. Brannt. Illus- 
trated by 25 engravings. i2mo. 177 pages . . . ^1.50 

WALL. — Practical Graining : 

With Descriptions of Colors Employed and Tools Used. Illustrated 
by 47 Colored Plates, Representing the Various Woods Used in 
Interior Finishing. By William E. Wall. 8vo. . ;?2.5o 

WALTON.— Coal-Mining Described and Illustrated: 

By Thomas H. Walton, Mining Engineer. Illustrated by 24 large 
and elaborate Plates, after Actual Workings and Apparatus. #5.00 



S8 HENRY CAREY BAIRD & CO.'S CATALOGUl. 

WARE.— The Sugar Beet. 

\ Including a History of the Beet Sugar Industry in Europe, Varietia 
of the Sugar Beet, Examination, Soils, Tillage, Seeds and Sowings 
Yield and Cost of Cultivation, Harvesting, Transportation, Conserva» 
tion, Feeding Qualities of the Beet and of the Pulp, etc. By Lewh 
S. Ware, C. E., M. E. Illustrated by ninety engravings. 8vo. 

WARN.— The Sheet-Metal Worker's Instructor: 
For Zinc, Sheet-Iron, Copper, and Tin-Plate Workers, etc. Contain- 
ing a selection of Geometrical Problems ; also. Practical and Simple 
Rules for Describing the various Patterns required in the different 
branches of the above Trades. By Reuben H. Warn, Practical 
Tin-Plate Worker. To vi^hich is added an Appendix, containing 
Instructions for Boiler-Making, Mensuration of Surfaces and Solids, 
Rules for Calculating the Weights of different Figures of Iron and 
Steel, Tables of the Weights of Iron, Steel, etc. Illustrated by thirty- 
two Plates and thirty-seven Wood Engravings. 8vo. . ^3.00 

WARNER.— New Theorems, Tables, and Diagrams, for the 
Computation of Earth-work : 
Designed for the use of Engineers in Preliminary and Final Estimates, 
of Students in Engineering, and of Contractors and other non-profes. 
sional Computers. In two parts, with an Appendix. Part I. A Prac- 
tical Treatise; Part II. A Theoretical Treatise, and the Appendix. 
Containing Notes to the Rules and Examples of Part I. ; Explana- 
tions of the Construction of Scales, Tables, and Diagrams, and a 
Treatise upon Equivalent Square Bases and Equivalent Level Heights. 
The whole illustrated by numerous original engravings, comprising 
explanatory cuts for Definitions and Problems, Stereometric Scales 
and Diagrams, and a series of Lithographic Drawings from Models i 
Showing all the Combinations of Solid Forms which occur in Railroad 
Excavations and Embankments. By John Warner, A. M., Mining 
and Mechanical Engineer. Illustrated by 14 Plates. A new, revised 
and improved edition. 8vo ^4-00 

WATSON.— A Manual of the Hand-Lathe : 

Comprising Concise Directions for Working Metals of all kinds. 
Ivory, Bone and Precious Woods; Dyeing, Coloring, and French 
Polishing; Inlaying by Veneers, and various methods practised to 
produce Elaborate work with Dispatch, and at Small Expense. By 
Egbert P. Watson, Author of " The Modern Practice of American 
Machinists and Engineers." Illustrated by 78 engravings. $l.SO 

WATSON. — The Modern Practice of American Machinists and 
Engineers : 
Including the Construction, Application, and Use of Drills, Latha 
Tools, Cutters for Boring Cylinders, and Hollow-work generally, with 
the most Economical Speed for the same ; the Results verified by 
Actual Practice at the Lathe, the Vise, and on the Floor. Together 



HENRY CAREY BAIRD & CO.'S CATALOGUE. 29 

with Worksl^op Management, Economy of Manufacture, the Steam* 
Enguie, Boilers,, Gears, BeUing, etc., etc. By Egbert P. Watson. 
Illustrated by eighty-six engravings. i2mo. . . . ' $2.^0 

UTATSON.— The Theory and Practice of the Art of Weaving 
by Hand and Power • 
With Calculations and Tables for the Use of those connected with the 
Trade. By John Watson, Manufacturer and Practical Machine- 
Maker. Illustrated by large Drawings of the best Power Looms. 
8vo. . . . • ^6.00 

WATT.— The Art of Soap Making : 

A Practical Hand-book of the Manufacture of Hard and Soft Soaps, 
Toilet Soaps, etc., including many New Processes, and a Chapter on 
the Recovery of Glycerine from Waste Leys. By Alexander 
Watt. 111. i2mo. ^300 

WEATHERLY.— Treatise on the Art of Boiling Sugar, Crys« 
tallizing, Lozenge-making, Comfits, Gum Goods, 
And other processes for Confectionery, etc., in which are explained, 
in an easy and familiar manner, the various Methods of Manufactur. 
i«g every Description of Raw and Refined Sugar Goods, as sold by 
ConfectioMers and others. l2mo $1.50 

WIGHTWICK.— Hints to Young Architects: 
Comprismg Advice to those who, while yet at school, are destined 
to the Profession; to such as, having passed their pupilage, are about 
to travel ; and to those who, having completed their education, are 
about to practise. Together with a Model Specification involving a 
great variety of instructive and suggestive matter. By George 
Wight'wick, Architect. A new edition, revised and considerably 
enlarged; comprising Treatises on the Principles of Construction 
and Design. By G. HusKissoN Guillaume, Architect. Numerous 
Illustrations. One vol. i2mo $2.0(t 

9\nLL>. — Tables of Qualitative Chemical Analysis. 
With an Introductory Chapter on the Course of Analysis. By Pro* 
fessor Heinrich Will, of Giessen, Germany. Third American* 
from the eleventh German edition. Edited by Charles F. HlMES^ 
Ph. D., Professor of Natural Science^ Dickinson College, CarHsle, Pa. 
8vo. . . • ^1.50 

WILLIAMS.— On Heal and Steam: 
Embracing New Views of Vaporization, Condensation, and Explo> 
sion. By Charles Wye Williams, A. I. C. E. Illustrated 8vo. 

$3 5<» 

WILSON.— A Treatise on Steam Boilers : 

Their Strength, Construction, and Economical Working. By RoBERt 
Wilson. Illustrated i2mo ^2,50 

i/VILSON.- First Principles of Political Economy : 
With Reference to Statesmanship and the Progress of Civilization. 
By Professor W. D. Wilson, of the Cornell University. A new and 
revised edition. i2mo ^1.50 



yo HENRY CAREY BAIRD & CO.'S CATALOGUE. 

WOHLER. — A Hand-Book of Mineral Analysis : 

By F. WoHLER, Professor of Chemistry in the University of Gottin- 
gen. Edited by Henry B. Nason, Professor of Chemistry in the 
Renssalaer Polytechnic Institute, Troy, New York. Illustrated. 
i2mo. .......... #3.00 

WORSSAM.— On Mechanical Saws : 

From the Transactions of the Society of Engineers, 1869. By S. W. 
WoRSSAM, Jr. Illustrated by eighteen large plates. 8vo. $2.50 



RECENT ADDITIONS. 

ANDERSON. — The Prospector's Hand-Book: 

A Guide for the Prospector and Traveler in Search of Metal Bearing 
or other Valuable Minerals. By J. W. Anderson. 52 Illustrations. 
i2mo ^1.50 

BEAUMONT.— Woollen and Worsted Cloth Manufacture: 

Being a Practical Treatise for the use of all persons employed in the 
manipulation of Textile Fabrics. By Robert Beaumont, M. S. A. 
With over 200 illustratiorfe, including Sketches of Machinery, 
Designs, Cloths, etc. 391 pp. i2mo #2.00 

BRANNT.— The Metallic Alloys : 

A Practical Guide for the Manufacture of all kinds of Alloys, Amal- 
gams and Solders used by Metal Workers, especially by Bell Founders, 
Bronze Workers, Tinsmiths, Gold and Silver Workers, Dentists, etc., 
etc., as well as their Chemical and Physical Properties. Edited 
chiefly from the German of A. Krupp and Andreas Wildberger, with 
additions by Wm. T. Brannt. Illustrated. i2mo. ^3-00 

BRANNT. — A Practical Treatise on the Manufacture of Vine- 
gar and Acetates, Cider, and Fruit- Wines ; 
Preservation of Fruits and Vegetables by Canning and Evaporation ; 
Preparation of Fruit-Butters, Jellies, Marmalades, Catchups, Pickles, 
Mustards, etc. Edited from various sources. By WiLLlAM T. 
Brannt. Illustrated by 79 Engravings. 479 pp. Svo. ^5.00 
BRANNT.— The Metal Worker's Handy-Book of Receipt? 
and Processes : 
Being a Collection of Chemical Formulas and Practical Manipula- 
tions for the working of all Metals ; including the Decoration and 
Beautifying of Articles Manufactured therefrom, as well as their 
Preservation. Edited from various sources. By WiLLIAM T. 
Brannt. Illustrated. i2mo. ^2.50 



HENRY CAREY BAIRD & CO.'S CATALOGUE. 31 

DEITE.— A Practical Treatise on the Manufacture of Per- 
fumery : 

Comprising directions for making all kinds of Perfumes, Sachet 
Powders, Fumigating Materials, Dentifrices, Cosmetics, etc., with a 
full account of the Volatile Oils, Balsams, Resins, and other Natural 
and Artificial Perfume-substances, including the Manufacture of 
Fruit Ethers, and tests of their purity. By Dr. C. Deite, assisted 
by L. BoRCHERT, F. Eichbaum, E. Kugler, H. Toeffner, and 
other experts. From the German, by Wm. T. Brannt. 28 Engrav- 
ings. 358 pages. 8vo. 13-00 

ED\A7ARDS. — American Marine Engineer, Theoretical and 
Practical : 
With Examples of the latest and most approved American Practice. 
By Emory Edwards. 85 illustrations. i2mo. . . ^2.50 

EDWARDS. — 600 Examination Questions and Answers ; 

For Engineers and Firemen (Land and Marine) who desire to ob- 
tain a United States Government or State License. Pocket-book 

form, gilt edge ^1.50 

POSSELT.— Technology of Textile Design : 

Being a Practical Treatise on the Construction and Application of 
Weaves for all Textile Fabrics, with minute reference to the latest 
Inventions for Weaving. Containing also an Appendix, showing 
the Analysis and giving the Calculations necessary for the Manufac- 
ture of the various Textile Fabrics. By E. A. PosSELT, Head 
■ Master Textile Department, Pennsylvania Museum and School of 
Industrial Art, Philadelphia, with over 1000 illustrations. 29a 
pages. 4to ' $5-oo 

POSSELT.— The Jacquard Machine Analysed and Explained: 
With an Appendix on the Preparation of Jacquard Cards, and 
Practical Hints to Learners of Jacquard Designing. By E. A. 
Posselt. With 230 illustrations and numerous diagrams. 127 pp. 
4to. . ^3.00 

POSSELT.— The Structure of Fibres, Yarns and Fabrics : 
Being a Practical Treatise for the Use of all Persons Employed in 
the Manufacture of Textile Fabrics, containing a Description of the 
Growth and Manipulation of Cotton, Wool, Worsted, Silk, Flax, 
Jute, Ramie, China Grass and Hemp, and Dealing with all Manu- 
facturers' Calculations for Every Class of Material, also Giving 
Minute Details for the Structure of all kinds of Textile Fabrics, and 
an Appendix of Arithmetic, specially adapted for Textile Purposes. 
By E. A. Posselt. Over 400 Illustrations, quarto. . ^10.00 

RICH.— Artistic Horse-Shoeing: 

A Practical and Scientific Treatise, giving Improved Methods of 
Shoeing, with Special Directions for Shaping Shoes to Cure Different 
Diseases of the Foot, and for the Correction of Faulty Action in 
Trotters. By George E. Rich. 62 Illustrations. 153 pages. 
i2mo ^i°oo 



32 HENRY CAREY BAIRD & CO.'S CATALOGUE. 

RICHARDSON.— Practical Blacksmithing : 

A Collection of Articles Contributed at Different Times by Skilled 
Workmen to the columns of "The Blacksmith and Wheelwright," 
and Covering nearly the Whole Range of Blacksmithing, from the 
Simplest Job of Work to some of the Most Complex Forgings. 
Compiled and Edited by M. T. Richardson. 

Vol.1. 2IO Illustrations. 224 pages. l2mo. . . ;gi.oo 

Vol. II. 230 Illustrations. 262 pages. l2mo. . . ^i.oo 
Vol. III. 390 Illustrations. 307 pages. i2mo. . . ;gi.oo 
Vol. IV. 226 Illustrations. 276 pages. i2mo. , . ^i.oo 

RICHARDSONr— The Practical Horseshoer: 

Being a Collection of Articles on Horseshoeing in all its Branchef 
which have appeared from time to time in the columns of " 1 he 
Blacksmith and Wheelwright," etc. Compiled and edited by M. T. 
Richardson, i 74 illustrations ^i.oo 

ROPER. — Instructions and Suggestions for Engineers and 
Firemen : 
By Stephen Roper, Engineer. i8mo. Morocco . ;g2.oo 

ROPER.— The Steanti Boiler: Its Care and Management: 
By Stephen Roper, Engineer. i2mo., tuck, gilt edges. $2.00 

ROPER.— The Young Engineer's Own Book: 

Containing an Explanation of the Principle and Theories on which 
the Steam Engine as a Prime Mover is Based. By Stephen Roper, 
Engineer. 160 illustrations, 363 pages. i8mo., tuck . ^3.00 

ROSE. — Modern Steam- Engines: 

An Elementary Treatise upon the Steam-Engine, written in Plain 
language ; for Use in the Workshop as well as in the Drawing Office. 
Giving Full Explanations of the Construction of Modern Steanv 
Engines: Including Diagrams showing their Actual operation. To- 
gether with Complete but Simple Explanations of the operations of 
Various Kinds of Valves, Valve Motions, and Link Motions, etc., 
thereby Enabling the Ordinary Engineer to clearly Understand the 
Principles Involved in their Construction and Use, and to Plot out 
their Movements upon the Drawing Board. By Joshua Rose. M. E. 
Illustrated by 422 engravings. 4to., 320 pages . . JS6.00 

ROSE.— Steam Boilers: 

A Practical Treatise on Boiler Constmction and Examination, for the 
Use of Practical Boiler Makers, Boiler Users, and Inspectors; and 
embracing in plain figures all the calculations necessary in Designing 
or Classifying Steam Boilers. By Joshua Rose, M. E. Illustrated 
by 73 engravings. 250 pages. 8vo ^2.50 

SCHRIBER.— The Complete Carriage and Wagon Painter: 
A Concise Compendium of the Art of Painting Carriages, Wagons, 
and Sleighs, embracing Full Directions in all the Various Branches, 
including Lettering, Scrolling, Ornamenting, Striping, Varnishing, 
and Coloring, with nurnei-ous Recipes for Mixing Colors. 73 Illus- 
trations. 177 pp. i2mo ;^i.oa 



Lr; 



